UC-NRLF B 3 HE SE1 LIBRARY UNIVERSITY OF CALIFORNIA. 1^\ ^ionsNo.VO ff^. QMS No. V A TREATISE INDUSTRIAL PHOTOMETRY WITH SPECIAL APPLICATION TO ELECTRIC LIGHTING BY A. PALAZ, Sc.D. PROFESSOR OF INDUSTRIAL ELECTRICITY IN THE SCIENCE FACULTY (ENGINEERING SCHOOL) OF THE UNIVERSITY OF LAUSANNE AUTHORIZED TRANSLATION FROM THE FRENCH BY GEORGE W. PATTERSON, JR., M.A., B.S. ASSISTANT PROFESSOR OF PHYSICS IN THE UNIVERSITY OF MICHIGAN AND MERIB ROWLEY PATTERSON, B.A. NEW YORK D. VAN NOSTRAND COMPANY LONDON SAMPSON LOW. MARSTON & COMPANY, LIMITED 1894 Engineering Library COPYRIGHT, 1894, BT D. VAN NOSTRAND COMPANY. TYPOC.K \I-HY BY J. S. GUSHING & Co., I'OSTON. TRANSLATORS' PREFACE. DR. PALAZ'S Traite de Photometric Industrielle Specialement Appliquee d L'Edairage Electrique was published in Paris in 1892. It is in great part a compilation of facts and experiments by the best authorities, and contains valuable data for the student in electricity and for those specially interested in the subject of electric lighting. No work to be compared with it has, as far as we know, appeared up to this time, and the great need of such a work, both in colleges and technical schools as a text-book and in the interests of electric lighting in general, seems to warrant its translation into English. In some cases, where different methods, employed at the Uni- versity of Michigan, could also be used with advantage, the trans- lators have noted the fact by references to the Appendix, which further contains some additional information on the general subject. Besides this work, Professor Palaz is the author of a work on Industrial Electricity (Cours d'Electricite Industrielle), being a series of lectures given to the engineers of the Jura-Simplon Railway Company in 1892. Adrien Palaz was born July 20, 1863, at Riex, in French Switzerland. After studying in the gymnasia of Burgdorf and Lausanne, he entered, in 1880, the Federal Polytechnic School, where he paid particular attention to mathematics, mechanics, and physics. After receiving his diploma, he remained in the school to pursue special studies in electricity in the electro-technical labora- iv TRANSLATORS' PREFACE. tory of Professor H. F. Weber. In 1885 lie received the degree of Doctor of Science from the University of Zurich. In the same year, M. Palaz entered the Central Telephonic Service of the Swiss Confederation at Berne ; but in 1886 accepted a position in the Bureau Internationale des Poids et Mesures at Sevres, and later became one of the editors of La Lumiere Elec- trique. In 1889, he was called to a professorship at the University of Lausanne, where he now occupies the position of Professor of Industrial Electricity. Dr. Palaz was one of the Swiss members of the chamber of delegates at the Chicago Electrical Congress of 1893. PREFACE. SINCE the introduction of the electric light, the public has been attracted by the advantages of an abundant illumination, and its requirements have become greater and greater, while the stimulus given the lighting industry has become the more active. The development of electric lighting has directed a great deal of research to the present conditions of the production of light, and to the best methods of measurement and distribution. The result has been a complete transformation in photometric methods, which now constitute an important whole. But as the reports of this research are scattered in special journals, both French and foreign, to make use of them is very difficult, if not ^impossible. This it is which has led me to co-ordinate the acquired results and to mold them into a homogeneous whole, in order to furnish the engineer charged with the installation and operation of lighting apparatus, the varied information of which he has need. My task has been made easy by the fact that since 1887 I have fol- lowed the progress of photometric methods in the various articles which I have published in the journal La Lumiere Electrique. There does not exist, so far as I know, any French work on industrial photometry; we must be content with the scanty infor- mation contained in special chapters of treatises devoted to light- ing by gas or by electricity. In Germany, a small manual by Kriiss, Die Electrotechnisclie Photometric, has had a certain success which led me to form the project of making a French translation of it. But since the date of its publication (1885) this work has, to a certain extent, become antiquated in consequence of the v Vi PREFACE. great progress resulting from the numerous researches of these last years; further, some parts are somewhat incomplete. Accord- ingly, I gave up this first plan, without, however, abandoning the idea of publishing a work on the subject. It is this work which I now present to the public, in the hope that it may render some service to all those, electrical engineers or gas engineers, who are concerned with the complex questions of lighting. I am fully conscious of the imperfections of my work, the first of this extent I shall be particularly grateful to all who will kindly communicate to me their observations or their criticisms. I have dwelt with great care on the numerous photometric apparatus invented especially during these last years, in order to indicate what a variety of methods and apparatus are at present at our disposal in photometry. This variety of apparatus has not prevented me from studying in detail the practical apparatus in current use, among others the photometers of Foucault, Bunsen, and Lunimer and Brodhun. The chapter devoted to photometric standards is very full; we cannot insist too strongly on the importance of an easy and exact reproduction of the light-standard. It has appeared to me indis- pensable to place before the eyes of the reader the most accurate results furnished by the numerous photometric standards which have been used up to the present. The various apparatus auxiliary to practical photometry are considered in the fourth chapter; in the fifth, I have treated the photometric properties of incandescent and arc-lamps, and have completed these data by remarks on common light-sources, and on the progress to be realized in the production of artificial light. A chapter on the distribution of lighting completes the work. This chapter is necessarily somewhat incomplete, for both from the physical and constructive points of view, artificial lighting, public and private, would demand study for itself; but it has been necessary to limit myself in order not to exceed, beyond measure, the bounds set for my work. PREFACE. Vii I have indicated the principal bibliographical sources of the memoirs which I have mentioned, in order to place the reader desirous of completing the study of a special problem, in a position to have recourse to the originals. I have set myself a limit, in order not to overload the work with bibliographical notices, and it has seemed to me useless to reproduce, at the end of the volume, a complete bibliography of the problems of photometry, and the list of the numerous memoirs consulted. A. PALAZ. LAUSANNE, December, 1891. CONTENTS. CHAPTER L PAGE PRINCIPLES OF PHOTOMETRY ..'' 1 CHAPTER IL PHOTOMETERS ....... ,. e 25 CHAPTER IIL PHOTOMETRIC STANDARDS . . . - ' ff .106 CHAPTER IV, GENERAL EQUIPMENT AND AUXILIARY APPARATUS-OF PRACTICAL PHOTOMETRY . . . . . . . ' ' . , .174 CHAPTER V. ELECTRIC LIGHTS . . ... . . , c 195 *. CHAPTER VI. THE DISTRIBUTION AND MEASUREMENT OF ILLUMINATION - 270 < APPENDIX . 309 INDEX . ,319 PHOTOMETRY. CHAPTER I. PRINCIPLES OF PHOTOMETRY. The Fundamental Photometric Law. 1. Common sources of light, e.g< flames, incandescent bodies, the voltaic arc, etc., have finite dimensions ; but to establish the funda- mental law of photometry which Bouguer and Lambert were the first to discover, it is necessary to consider first a theoretical source of light formed by a luminous point. It is then possible to gener- alize the results obtained by applying them to luminous sources of finite dimensions. FIG. 1. Let, be a source of light so small that it mafy be considered as concentrated at a point. If this is placed at the center of a spheri- cal shell S' (Fig. 1), having a radius r' and a homogeneous and 1 2 PHOTOMETRY. uniform surface (covered, for example, with a layer of white-lead), all parts of the inner surface will appear equally illuminated. The source emits a determined quantity of light Q. The whole of this quantity of light is received by the surrounding shell whose surface is 47r?-' 2 . Since all parts of the surface appear equally illu- minated, a unit area situated anywhere on the surface will receive a quantity of light A second concentric spherical shell of radius r" will also receive the same quantity of light Q, but a unit surface of this sphere will receive only the quantity q= 3 . 47rr" 2 From this it follows that ~^i = ^' That is to say, the quantities of light received per unit area on concentric spheres of radii r' and r" are inversely proportional to the squares of the radii r' and r". ( The Law of Distances.) 2. Further let us consider a closed surface of any form situated within the spherical shell S'. This surface evidently receives the same quantity of light Q as the surrounding surface. Let us cut off any portion of this surface dS by a cone having its vertex at the center O of the sphere ; let dO be the solid angle correspond- ing to dS ; that is to say, the corresponding portion of the surface of a sphere having a radius of unity. The quantity dq of light received on dS is then the same as that received by the element dQ, ; now this receives the quantity of light then dq = --dQ. 4?r But -z- is a constant which measures the emission of light from 4?r the source ; this is called the total intensity, and is designated by the letter /; from this it follows that PRINCIPLES OF PHOTOMETRY. The preceding equation then becomes dq = If cZO = 1, then dq = I-, that is to say, the total intensity is equal to the quantity of light emitted in a solid angle equal to unity. Let us call ds the projection of the element dS on the plane per- pendicular to the radius vector r of the element dS, i being the angle between the normal to dS and the radius vector, and we have ds = dS cos i } 2- l r +-L_ j ds dScosi then dfl = = - , consequently dq = IdQ = ; (3) that is, the quantity of light received by an element of surface dS, whose normal makes an angle i with the direction of the luminous ray, is proportional to the cosine of the angle of incidence i. Let the intensity of illumination of a surface at a given point be the ratio of the quantity of light received by the element dS of the surface at this point to the area of this element; intensity of illumination is generally designated by e. Then ~~ If the surface dS is equal to unity, e = dq ; the intensity of illu- mination may then also be considered as being the quantity of light received by a unit surface. 3. Instead of considering the luminous source concentrated at a point, let us assume that it has the form of a sphere of radius R. Each element dS of the surface furnishes part of the luminous emis- sion, and the quantity of light emitted by this surface dS is PHOTOMETRY. In these formulae, Q represents the total quantity of light emitted by the source, and / its total intensity ; if dS = 1, it follows that do- q ~ The expression ^ = , which represents the quantity of light ~ R emitted normally by a unit of surface of the luminous source, is called the intrinsic intensity, or the brilliancy, of the source; this is designated by the letter i * ; then it follows that Q = 4 irR- i. The total quantity of light Q emitted by a luminous source is therefore equal to the product of its brilliancy by its surface. The total intensity /may then be deduced by the aid of equation (2). Let us consider the source of light limited by a plane surface AB ; let us suppose the intrinsic intensity i constant at all points of the source ; the quantity of light emitted by the If surface S of the plane AB, determined by / the opening of the screen E, is equal to iS, and the emission of light takes place normally to the plane AB. Now let the surface AB be inclined and * A placed in the position A'B'j a portion of the surface S ' of the plane AB corresponds to the opening S of the screen. It is shown by experiment that the quan- tity of light traversing the opening of the screen does not change. So if e designates the angle between the planes AB and A'B', we have I and since the light emitted has not varied, and since the surface of emission has increased in the ratio of 1 to cose, the intrinsic inten- sity i must have diminished in the same ratio ; it then follows that i= i cose. * The same letter, i, is used to designate the angle of incidence and the intrinsic intensity, because there is no possibility of confusion. PRINCIPLES OF PHOTOMETRY. 5 This empirical law, given for the first time by Lambert*, is known under the name of the law of the cosine. Another proof of the accuracy of the law of the cosine follows from the fact that an incandescent metallic sphere appears in the dark as a uniformly luminous disc. Any element of the surface of the visible he mi sphere then sends to the eye the same quantity of light as that which would be emitted normally by the projection of the element on the base of the hemisphere. It should be remarked, however, that the law of the cosine is exact only in so far as phenomena of diffraction and reflection may be neglected, and where the angle e is very small. This should be considered as an approximate law, and not one rigorously true. Certain recent experiments of Seeligerf, in particular, have shown that the deviations of this law from the results of direct observa- tion frequently exceed one per cent, even for very small angles of incidence. 4. The fundamental law of photometry. We may summarize the preceding laws in a single formula. Let dS be an infinitesimal element of a luminous surfac.e at a point where the intrinsic inten- sity is i ; let dS' be an infinitesimal element of a second surface S' illuminated by the first ; let us call d the distance between the two elements, e the angle that the line joining them makes with the normal to dS, and e' the angle which the same line makes with the normal to d/S'. The quantity of light emitted by d/S and received by d/S' is given by the formula cose cose'. Assuming that the dimensions of a quantity of light are the same as those of a quantity of heat, and taking account of the relations [d] * Lambert, Photometria sive de mensura et gradibus luminis, 1760. t Berichte der bay. Acad. der Wiss., 1888, p. 201, and Lum. tfl., Vol. XXV. p. 615. 6 PHOTOMETRY. we have the following dimensions, dim. Q = dim. /= \_ML?T-*~\, dim. i = dim. e = \_MT~*~\. The choice of the unit for the intensity / determines also the choice of the unit of brilliancy and the unit of illumination, as the preceding formulae show. We shall have occasion to revert to this special point when we take up the study of the usual sources of light and the problems of the distribution of light. The Intensity of Light according to the Undulatory Theory. 5. According to the undulatory theory, light is the result of the vibratory movement of the ether propagated along a straight line. The equation of this movement is In this equation v is the velocity of a molecule of ether of mass /A at the point considered and at the time t ; this point is situated at a distance d from the luminous source where the maximum amplitude is Vi ; the period of the vibratory movement is T, and the relation of the wave-length \ to the velocity of propagation c of the vibratory movement is It is known that the color of light depends upon the value of the wave-length. A light is said to be monochromatic when it emits vibrations of ether of the same wave-length only. Ordinary luminous bodies emit complex light ; that is, they produce a com- plex vibratory movement. This complex movement is formed by the superposition of simple undulatory movements, each corresponding to a single wave-length ; the undulatory movements of the ether possess the property of having the velocity of propagation cf = j inde- pendent of the wave-length ; at least, the most careful experiments indicate this. PRINCIPLES OF PHOTOMETRY. 1 The quality of the light from a given source depends on the wave-length of the radiations emitted, and 011 the proportion in which the vibrations of the different wave-lengths unite in the formation of the complex light emitted. The intensity of vibratory movement at a given point where the superficial element dS is situated is equal to the vis viva of the molecules of ether /* which are on this element at the time t ; but this vis viva varying continually, we consider the mean vis viva of these molecules during the period of one oscillation to represent this intensity ; we have and, replacing v by its value, we obtain The intensity of a monochromatic luminous vibration is then a quantity mathematically defined; we see that it is proportional to the square of the maximum amplitude v^ But we cannot deter- mine this intensity directly, for it is not possible to measure the quantities /x and t^j we may ignore the mass /x, since this factor disappears in the comparison of two luminous intensities. The comparison of two monochromatic luminous intensities then reduces to the comparison of the amplitudes of their vibratory move- ment. Unfortunately it is not possible to measure this element as, for example, we measure wave-lengths, and so it is necessary, in order to measure the intensity of a luminous radiation, to have recourse to the actions that it exerts on various substances and phenomena. The Various Actions of Light. 6. Without taking into account the action of light on the elec- tric and magnetic properties of certain bodies and on certain electrical phenomena, we may distinguish three different kinds of actions of light, calorific, chemical, and illuminating. For a long time there have been distinguished in the light from any given source, in sunlight for instance, chemical, calorific, and illuminating rays. This distinction is entirely arbitrary, and the curves which represent the variations of intensity relative to the 8 PHOTOMETRY. chemical, calorific, and luminous rays of a given light are only in reality the graphic representation of absorption-spectra of substances which have been used in their study ; for example, salts of silver, lampblack, and the retina. The presence of waves of ether of a determined length is proved by the aid of one of the phenomena mentioned above. We know, for example, that it is only vibrations of the ether whose wave- length is included between 0.360 /A* and 0.810 p that act on the eye and produce an impression of light. Other vibrations, whose wave-lengths are greater or smaller, have no luminous action on the retina, and can only be proved to exist by the action which they exert on other substances, an action which is calorific or chemical ; however, the fact that it is impos- sible, by any given process, to observe the presence of vibrations of a determined wave-length in a luminous pencil does not per- mit us to conclude that they do not exist, for they frequently require exceedingly sensitive methods and apparatus to prove their existence. [Radiations of small wave-length (ultra-violet) are generally shown to exist by their chemical action, in the same way that radiations of considerable wave-length (infra-red) are shown to exist by their calorific action. However, we should not conclude that the calorific action of the first and the chemical action of the second are null ; for a ray of determined wave-length may exert at the same time the three actions, chemical, calorific, and luminous. Below there will be found certain data relative to the principal radiations which may be shown to exist by means now used. Quality of Radiations and Means of recognizing them. Ultra-violet rays (photography). Visible radiations (the eye). Beginning of the ultra-red (phosphorescence) . Wave-Lengths in Microns. Character of the Vibratory Movement. 0.185 Extreme ray of the aluminium spectrum obtained by a spark from induction coil. (Cornu.) 0.295 Extreme limit of the solar spectrum at sea- level. (Cornu.) 0.360 Limit of lavender light, visible for normal eyes. 0.810 Extreme limit of dark red light. 1 Extreme possible limit of wave-length in the ultra-red. (Draper. ) 1 micron = 1 n = 0.001 mm. PRINCIPLES OF PHOTOMETRY. 9 Quality of Kadiations and Wave-Lengths Means of recognizing them. in Microns. Character of the Vibratory Movement. Thermal action 2.7 Sensible limit of solar rays which pene- (bolometer). trate the atmosphere at Allegheny. (Langley.) 5.3 Limit with prism of rock salt. 7.5 Approximate position of the maximum of Radiations from terres- trial sources (bolometer). a black surface at 100 C. 11 Black surface at C. 30 Approximate estimation of the minimum value of the longest heat-wave with a prism of rock salt. Sound vibrations (ear). 14,000 The shortest perceptible wave-length (Savart, 24,000 vibrations per second). This table shows that the extent of the normal spectrum percep- tible to the eye is very narrow ; this extent does not exceed fifteen thousandths of the spectrum perceptible by photographic and calori- metric methods. The Photometric Action of Light. 7. From a photometric point of view, the only radiations which are to be taken into account are those which are perceptible to the eye. Now all the vibrations with wave-lengths above 0.36 ^ (about), and principally those above 0.81 /w., contribute to-the calorific action of a luminous pencil, while it is only those whose vibrations are included between the above two limits which act upon the eye. It is the same with the chemical action of a luminous pencil ; in this case it is especially those radiations whose wave-lengths are below 0.36 /A which produce the greatest part of the total chemical action of the pencil. We see then that chemical or calorific phenomena of light cannot be used to measure its photometric intensity, especially when the nature of the work executed by the luminous pencil on a body work which is shown by elevation of temperature or by chemical decomposition depends on work already executed on other bodies by the same pencil. To illustrate, let us take a luminous pencil of well-determined intensity, and pass it through an alum solution ; the photometric action of the luminous pencil will not vary noticeably, while its calorific action will be considerably diminished. 10 PHOTOMETRY. If, then, we should compare the photometric action of a lumi- nous pencil, after its passage through an alum solution, with that of another luminous pencil which has not passed through any solution of this kind, by comparing their calorific actions, we would make a great error. The same remark applies to the other physical phenomena on which light has an influence (variation of the electrical resistance of selenium under the influence of light, variation of the magnetic moment of a bar-magnet, actino-electric discharges, etc.). The luminous intensity of a pencil of light differs essentially from the intensity of vibratory movement defined by the undulatory theory. From the photometric point of view, light is manifested by a sensation, by a simple physiological phenomenon. The lumi- nous intensity of a pencil of light is not the energy of the vibratory movement of the ether, but only the action of this energy on our visual organ. Sensibility of the Eye for Photometric Observations. 8. The eye is then the standard piece of apparatus for all photo- metric operations ; it is the photoscope required for every compari- son of intensity of two luminous bodies ; the eye here plays the same rdle as the galvanometer or the electrometer in electrical measurements by zero methods. We can therefore only tolerate for photometric measurements a healthy and well-formed visual organ. Furthermore, the obligatory employment of the eye imposes, in photometric measurements, a limit of precision determined by its sensibility. Since it is the eye alone which can appreciate the photometric qualities of a luminous pencil or of a given illumination, we do not measure, in reality, the luminous intensity of a source of light or the intensity of illumination of a surface, but the excitation pro- duced on the eye and the optic nerve. Now any one may prove that the visual organ is incapable of distinguishing whether an illu- mination is m or n times as great as another illumination ; the eye can only judge that one is greater than the other, but without being able to estimate their ratio. This fact, verified experimentally every day, is one of the consequences of a general law which gov- erns the greater part of the sensations. This is the psycho-physical law of Fechner, according to which the intensity of the sensation is proportional to the logarithm of the excitation *. * Helmholtz, Optique Physioloffique, p. 415. PRINCIPLES OF PHOTOMETRY. 11 It is known that in every sensation we denote by stimulus thresh- old the inferior limit, below which the stimulus is too slight to produce a perceptible sensation ; the maximum stimulus is the supe- rior limit, above which an increase in the intensity of the stimulus produces no increase in the intensity of the sensation. The value of the sensation which corresponds to the stimulus threshold is called the minimum sensation; that which corresponds to the maximum stimulus is called the maximum sensation; the name sensible value or physiological unit is also given to the stimulus threshold ; for this quantity is employed as unity in measurements of the stimulus. In the case where the equality of two illuminations is established, the physiological unit is the limiting value which the difference of the two illuminations should attain in order that this difference may be perceptible to the retina. To determine this quantity, we may proceed in the following manner invented by Bouguer : a white screen is illuminated by two equal sources of light (two equal candles), and a rod is placed in front of the screen, on which it projects two shadows (Kumford's photometer). One of the candles is moved away until the corre- sponding shadow ceases to be visible. Let a be the distance of the screen from the nearer light, b its distance from the farther light ; the intensities of illumination pro- duced on the screen by these two lights are in the inverse ratio of a 2 to 6 2 . Bouguer found - = - , while Fechner obtained - = ; it then 68 b 10 follows that Bouguer could distinguish -^ of the luminous intensity, and Fechner yi-g-. Arago observed that, by moving the candle, still smaller differences may be noticed, and thus found -yjy. Lastly, Helmholtz was able to distinguish differences of illumination of yi-g- between the concentric circles of a disc, and at times differences of y^. and even y^. The disc was then illuminated by diffuse daylight. In illumi- nating the disc by direct sunlight, perception of the differences of illumination became more difficult. The sensible value in the com- parison of two illuminations depends on the intensity of the illumi- nations or of the lights that are considered; it is maximum for a mean value, and smaller when the illuminations are too intense or too weak. Thus Masson found that the sensible value (stimulus threshold) was maximum when the luminous intensities to be compared were 1 2 PHO TOMETE Y. of the order of diffuse daylight ; he obtained, under these conditions, Y^g- for the threshold value of excitation ; that is, he was able to distinguish differences of illumination of even y i-g. The practical conclusion from this is that in photometric com- parisons we should so manage that we have to compare only illuminations whose intensity approximates the value of the illu- mination produced by diffuse daylight. The preceding shows, moreover, that the eye is incapable of appreciating the inequality of illumination of two contiguous sur- faces within about 0.01, even when the colors that are compared are identical, as in the measurements indicated above. This fact limits the precision of photometric measurements. From the moment when the difference of intensity of two lights, or the difference of illumination of two surfaces, has passed the sensible value corresponding to the observer and to the conditions of the experiment, the intensity of the sensation varies, according to the psycho-physical law of Fechner, verified by the numerous measurements of E. H. Weber. According to these measurements the increment of sensation dS is proportional to the ratio between .the increment of the excitation dl and the primitive excitation J; that is, fl T dS = k*, or, integrating, S = k log I C. The sensation S is null for an intensity of excitation equal to the sensible value 7 ; we have then and consequently S = k log IQ This formula, which expresses the psycho-physical law of Fech- ner, shows then that when the intensity of luminous excitation (illumination) passes from a given value to a value m times as great, the sensation increases in the ratio of a to (a + logm). These facts clearly explain why the eye is unable to appreciate with precision the ratio of the two luminous sensations produced by two different sources, but can appreciate only their equality. Variations of the Sensibility of the Eye with the Color of the Light. 9. The sensibility of the eye varies with the nature of the luminous rays ; all the preceding figures relative to the visual PRINCIPLES OF PHOTOMETRY. 13 sensibility of several observers, have reference to white light, but these values are no longer the same if the nature of the light changes. There is very little exact knowledge concerning the relative values of the stimulus threshold for the different regions of the spectrum. We give, however, the values obtained by Ebert (E) and his assistant (S) by the aid of a method giving sufficiently accurate results *. The following table gives the relative values of the stimulus threshold for five regions of the spectrum. They are given in the first double column. Color. Length of Wave in /u.. Relative Stimulus Threshold. Stimulus Threshold Keferred to the Same Energy of Vibratory Motion. E s E S Red 0.675 0.8 0.6 34 25 Yellow .... 0.590 2.3 2.0 17 15 Green .... 0.530 0.5 0.5 1 1 Bluish green . 0.500 1.2 0.8 2 1.3 Blue . . . 0.470 7.3 6.8 t 3 These values were obtained using an Argand gas-burner. To reduce them in terms of the normal solar spectrum, it will suffice to take into account the measurements of the relative energy in the different regions of the solar spectrum made, for instance, by Langley, and the measurements of the energy of the spectrum of a gas flame made by 0. E. Meyer. The numbers in the third double column are thus obtained. The sensibility of the excitation is then given by the reciprocals of the threshold values. The table shows that the sensibility of the luminous excitation is maximum for green and minimum for red. Consequently the energy of the vibratory movement, which contributes to the pro- duction of a luminous sensation, is maximum when the length of the wave is the same as that of radiations in the green region of the spectrum. That is to say, when A. is about 0.530 /x. These conclusions are confirmed by the very careful observations made by Langley f on the visual energy in the different regions of * Wiedemanns Ann., Vol. XXXIII. p. 136. Lum. til., Vol. XXVII. p. 139. t Lum. til., Vol. XXXI. p. 144. 14 PHOTOMETRY. the normal solar spectrum. He also found that the same quantity of vibratory movement produces in the green an impression 100,000 times as great as that which is produced in the dark red (0.750 /A). Below are the figures which represent the luminous sensation produced by the same quantity of energy in the various parts of the spectrum. The luminous sensation produced in the dark red (0.750 //,) is taken as unity. Violet. Blue. Green. Yellow. Orange. Red. Dark Red. Length of wave in /j.. Luminous sensation. 0.400 1600; 0.470 62,000 ; 0.530 100,000 0.580 28,000 ; 0.600 14,000 0.650 1,200 0.750 1. Composition of the Light emitted by Various Luminous Sources. 10. A body when heated sends forth rays, that is to say, it- causes a vibratory movement of the ether, the nature of which depends on the temperature. With Draper it was assumed, until within a few years, that all bodies begin to emit rays perceptible to the eye when their temperature reaches 525 C., and that these rays belong to the extreme red of the normal spectrum where the wave-lengths are greatest. Some years ago H. F. Weber* discovered that a solid body whose temperature is being raised, commences to emit light before it becomes incandescent. The first sensible trace of light in the spectroscope is a hazy, gray band which appears in that part of the spectrum which corresponds to the yellow and yellowish green. If the temperature continues to rise, the spectrum of the rays emitted by the heated body increases on both sides of this gray band. Weber found the first trace of light at 417 C. with gold, at 390 C. with platinum, and at 377 C. with iron. This phenomenon is easily explained by what has been shown above concerning the eye's sensibility, which is maximum for green rays ; consequently the first luminous ray emitted by a body just beginning to be luminous should appear in this region of the spectrum. Having passed the temperature at which the first rays are per- ceived, the brightness of the incandescent body increases very rapidly with the temperature. Kays of longer and shorter wave- * Sitzunysber. der Berliner Acad., 1887, p. 491 ; Lum.til., Vol. XXX. p. 31. PRINCIPLES OF PHOTOMETRY. 15 length are added to the yellow and yellowish green, and as complete incandescence is attained, the increase of rays of great refrangibility becomes very rapid. The spectrum of the light emitted by a body raised, for example, to a temperature of 720 C. includes all the colors up to a reddish orange (from the A to the C line) ; at 780 C. it extends to the bright orange (G), and at 1165 C. it includes the whole spectrum between the lines A and H. Above 1165 C. the ultra-violet rays, which are not perceptible to the eye, are to be added to the preceding. Below are the values obtained by Violle* for the luminous intensity of four different regions of the spectrum of a disc of plati- num raised to high temperatures ; the unit adopted for the rays of each color is the intensity of the corresponding rays in the spectrum of melting platinum. Temperature. C. A = 0.656 M. (C) A = 0.5892/01. (D) A = 0.536 M. (E= 0.527 M.) A = 0.482/u. (F = 0.416,m.) 775 0.00038 0.00007 0.00003 954 0.00197 0.00124 0.00073 1045 0.00645 0.00450 0.00271 0.00133 1500 0.303 0.271 0.225 0.155 1775 1.000 1.00000 1.000 1.000 If the intensity of the corresponding rays in the spectrum of the carcel lamp is taken as a unit, the following table is obtained : Temperature. A = 0.656. A = 0.5S92. A = 0.586. A = ft.48'2. 775 0.00300 0.00060 0.00030 954 0.01541 0.01105 0.00715 1045 0.0505 0.0402 0.0265 0.0162 1500 2.371 2.417 2.198 1.894 1775 7.829 8.932 9.759 12.16 These two tables show the rapidity with which the luminous inten- sity increases as the temperature is raised. For instance, the intensity of the rays having a wave-length of 0.589 p is more than * Comptes Rendus, Vol. LXXXVIII. p. 171, and Vol. XCII. p. 866. 16 PHOTOMETRY. eight hundred times as great at the temperature of melting plati- num (1775 C.) as it is at the temperature of melting silver (954 C.). It can be seen from, the second table how much more intense are the highly refrangible rays emitted by incandescent platinum than those of the carcel lamp. The higher the temperature rises, the more intense become the rays of short wave-length. If the temperature is low, rays of great wave-length preponderate, and the light' appears red. In order that light may be white like sunlight, it is necessary that the rays of the various wave-lengths should be combined in the same ratio as the corresponding rays of the normal solar spectrum. If the red rays are more intense than in the normal spectrum, the light appears red ; and in the same way it appears violet if the violet rays are more intense. In the following table are the values obtained by Crova * for the luminous intensity of rays of the same wave-length emitted by different sources, the luminous intensity of the wave whose length is 0.676 /x being taken as unity. Wave-length . 0.676 //, Voltaic arc . . 1.000 Drummond light 1.000 Carcel lamp . . 1.000 These values show that in the light of the carcel lamp the red rays are nearly sixty times as intense as the violet, while in the light of the voltaic arc they are only four times as intense, that is, one-fifteenth as much. Moreover, it is well known that the flame of the carcel lamp appears red beside the voltaic arc. Taking as a standard the rays of the carcel lamp, W. Pickering f found the following values for certain rays of different luminous sources. 0.605 /* 0.560^ 0.523 n 0.486 /* 0.459 it. 0.707 0.597 0.506 0.307 0.228 0.573 0.490 0.299 0.168 0.073 0.442 0.296 0.166 0.080 0.017 Kays of the Spectrum. C. D. b' Between F and G. Candle 73 100 104 134 Gas-light .... 74 100 103 125 Voltaic arc . . . . . 61 100 121 735 * Comptes Bendus, Vol. LXXXVII. p. 322. t Nature, Vol. XXV. p. 340. PRINCIPLES OF PHOTOMETRY. 17 Finally, 0. E. Meyer * obtained the following values, taking the rays emitted by a gas flame as a standard, and making the intensi- ties corresponding to the D line unity. Kays of the Spectrum. U. D. E. ! 0. Petroleum lamp . 0.66 1.00 1.40 1.00 Sunlight, direct . . . 4.07 1.00 0.43 0.15 Sunlight, diffused . . 1.25 1.00 0.50 0.41 Voltaic arc .... 1.10 1.00 0.40 0.10 Incandescent lamp . . 0.30 1.00 1.40 1.10 The above results are sufficient to allow the classification of sources of light according to the nature of the light which they emit. The units not being the same in the preceding tables, it is not possible to compare directly the values which they contain. We may, however, state that the usual sources of light can be classed as follows, with reference to the kind of light emitted : carcel lamp, candle, gas-light, petroleum lamp, incandescent plati- num, Drummond light, voltaic arc, sunlight. The Photometric Elements of Luminous Sources. 11. Definitions. The intensity of a source of light varies in general with the direction of the luminous rays. For a long time observers have limited themselves to considering only the luminous intensity in a horizontal plane passing through the center of the luminous body, that is, the horizontal luminous intensity ; the devel- opment of illumination by intensive burners and by the voltaic arc has required more attention to be paid to the problem, and new factors to be introduced into the study of a light-center. Thus there has been introduced the notion of mean spherical intensity,. which plays an important part in the comparison of the photometric qualities of light-centers. If we lay off in various directions lines passing through the luminous source, whose lengths measure the intensity of the rays emitted in those directions, the locus of the points thus obtained forms a surface called the photometric surface of the source. In arc-lights, for instance, the photometric surface may be con- * Monatsber. der Berliner Acad., 1880. [See article by H. G. Vogel, p. 801.] 18 PHO TOMETE Y. sidered in general as one of revolution about the common axis of the two carbons, although, in many cases, this condition is not per- fectly fulfilled, on account of defects in the homogeneity of the car- bons and in their centering. The meridian of the photometric surface has a well-determined form. In order to construct it, we measure the luminous intensity for inclinations not differing too much in the different azimuths. We choose, in general, inclinations varying by 10 degrees, and four azimuths differing by 90 degrees. We take, then, as the luminous intensity for a given inclination the mean of the values obtained for this inclination in the four azimuths. To construct the curve, we take as the unit of luminous intensity the maximum luminous intensity. The graphical construction is simplified by employing a sheet prepared in advance, formed of concentric circumferences described around the point A as center, having respectively for radii 0.1, 0.2, 0.3, etc., the line AP being taken as unity ; and ^>f . straight lines passing through the point A and making angles of 10 degrees, 20 degrees . . . , above and below the horizontal AH. Along these straight lines the corresponding luminous intensity is laid off in terms of the maximum intensity AE taken as unity. The line ABCDEF passing through the points thus determined is the meridian curve of the photometric surface of the center; it shows at a glance what is the relative intensity in any given direc- tion, AD for example. 12. Mean horizontal intensity. The mean horizontal intensity of a light-source is the mean of the values of the intensity, meas- ured in all directions in the horizontal plane passing through the source. Practically, it is sufficient to make these measurements in a certain number of symmetrical directions and to calculate the mean. If the photometric surface of a light-source is cut by a hori- zontal plane passing through the source, the curve of intersection represents the variations of the horizontal intensity. The mean horizontal intensity is then represented by the mean value of the radius vector of this curve. To determine practically the mean horizontal intensity of a light-center, it is sufficient to make meas- urements in a small number of different directions, four or eight for instance, symmetrically arranged. 13. Mean spherical intensity. The mean spherical intensity may be defined as the sum of the illuminations received by a sphere PRINCIPLES OF PHOTOMETRY. 19 of radius 1, concentric with the light-source, divided by the surface of the sphere. In other words, it is the intensity of the light-source rendered uniform, i.e. emitting luminous radiations of constant intensity in all directions. In the calculation of mean spherical intensity it is generally assumed that the photometric surface is a surface of revolution ; consequently the luminous intensity / is independent of the azimuth, and only varies with the inclination of the ray. This intensity is then a function of the inclination 6 to the horizontal ; consequently /=/(<>). The total intensity then will be the mean of the partial inten- sities relative to each direction. To obtain this mean, let us con- sider the part of the photometric surface comprised between the two parallels denned by the angles 9 and 6 + dO. These* two angles differing very little, we may suppose the intensity / constant. The quantity of light which falls 011 this zone of the photometric surface is equal to that which the corresponding zone of the unit sphere receives. Now the height of this zone being cos0 dO, its surface is equal to 2 ?r cos0 d9, and the quantity of light which it receives is given by the expression 2irIcos6dO. Consequently the total quan- tity of light received by a zone of the photometric surface and the C* corresponding zone of the sphere is equal to I 27rIcos6dO, O l and 2 being the relative inclinations of the parallels which limit the zone. The mean intensity of illumination of the zone will then equal the total quantity of light received divided by the surface ; that is, The mean spherical intensity is equal to the intensity of the mean illumination of the unit sphere, that is, to the total quantity of light received by the unit sphere divided by its surface ; which gives ~+f 27r/cos0d<9 Practically, the law according to which the intensity varies with the inclination is not simple enough to allow the integration to be 20 PHOTOMETRY. effected directly. We are obliged to effect it by approximation. The calculation is simplified by the employment of a curve which is deduced immediately from the meridian curve of the photometric surface in the following manner. 14. Calculation of mean spherical 'intensity. To obtain the dif- ferent points of this curve (Fig. 3) it is sufficient to draw, through the points where the prolongations of the radii AB, AC. AD, etc., meet the circumference, horizontal lines and to lay off on these, from the point where they meet the perpendicular P'Q' drawn at a distance 1 from the point A, lengths equal to the radii vectores which measure the relative intensities ; we have then bB' = AB, cC' = AC, etc. We may facilitate the construction by employing a sheet prepared in advance *. The length dm on the line P'Q' corresponding to the inclinations and 6 -\- dO is equal to cos0 dO, and the length dD' is equal to the intensity 7; consequently the surface dmM'D' is equal to IcosOdO. Then the product of this surface by 2?r represents the quantity * Comtes rendus des essais Photometriques a V exposition d? Anvers, en 1886, par M. Rousseau. PRINCIPLES OF PHOTOMETRY. 21 of light received by the zone corresponding to dO. It follows that the entire surface P'C'E'Q' is equal to I I cos0c?0, and multiplied f by 2-n- represents the total quantity of light received by the unit /.-H sphere. The mean spherical intensity being equal to 2?r f Jcos0 dO divided by the surface of the sphere (47r), is thus given by the expression - ^ Now the surface of the rectangle P'RSQ' is equal to 2, hence the mean spherical intensity is the ratio of the surface P'RSQ' to the surface P'C'E'Q'. The determination of the mean spherical intensity may then be made graphically; it is sufficient to evaluate the surface P'C'E'Q' by the aid of a plani- meter. We may, however, dispense with a graphic determination by effecting the calculation in the following manner : we replace the meridian curve of the photometric surface by a polygonal line having its angles at the points determined directly by observation, which is the same thing as regarding the mean luminous intensity of each zone as being equal to the arithmetical mean of the inten- sities I' and I" corresponding to the inclinations 0' and 0" of the circles at the bases of the zone ; the quantity of light received by this last is then '-^ = 2 7r(sin 0" - sin 0') J> + X " Making the measurements at the angles D 2 , 3 , .. O n , the quan- tity of light received by the total zone is equal to [ L (sin 2 - sin X ) 7l + /2 + (sin 0, - sin 2 ) - 2 -^ 2 2 J The surface of this zone being equal to 27r(sin0 n sii^), the corresponding mean intensity is equal to (sin 2 - sin 00 *** + . . . + (sin n - sin n _0 J - 1 + J " sin O sin 22 PHOTOMETRY. Supposing that 6 l equals ^, and U equals -f ^, we obtain the mean spherical intensity ; the denominator is then equal to 2. A knowledge of the exact distribution of light in the upper hemisphere has only a limited importance with respect to the illumination; this is especially the case with the arc-lamp. For this reason it is sufficient to determine the luminous intensity at intervals of 30 degrees in the upper hemisphere. In this case the formula which gives the mean hemispherical intensity (for the upper hemisphere) becomes, the area of its surface being 2 TT, sin30 -sin0 /7 , , v , sin 60 -sin 30% r , 2 \lrMv~' 2 ~^ 3 ' . sin 90 -sin 60 , T , . T ,, - o - ~\ 2 3 + -* 4> In the arc-lamp 7 4 (the intensity in the vertical direction) is null,.- and the formula may be written 0.250(7'! + 7' 2 ) + 0.183(7' 2 + 7' 3 ) + 0.067 7' 3 . Taking a difference of 10 degrees for the measurement in the lower hemisphere, the formula for mean hemispherical intensity becomes sinl0 -smO rx , sin 20 - sin 10 , r , n , t) T - ~ ' 2 "^40 r 2 or 0.0868(/ 1 +/ 2 ) + 0.0842 (J, + / 8 ) + 0.0790 (7 8 + J 4 ) + 0.0714(7 4 +/ 5 ) + 0.0616 ( J 5 + / 6 ) + 0.05 (7 6 + 7 7 ) + 0.0368(7 7 + / 8 ) + 0.0226 ( J 8 + / 9 ) + 0.0076 7 9 . If we wish to reduce the number of measurements from 9 to 6 (the intensity in the vertical direction being null), it is sufficient to make measurements at intervals of 15 degrees. We then have for the mean hemispherical intensity sin!5 sinO , T . , sin 30 - sin 15 , T . r x . - 2 -VI-H^H -- 2 -( / 2+7 3 )4-- or 0.1294(7 1 +/ 2 )+ 0.1206(7 2 +7 3 ) + 0.1036 (7 3 -f 7 4 ) + 0.0794 (7 4 +7 5 ) + 0.050 (7 5 + 7 6 ) + 0.017 7 6 . The preceding method of calculation was employed by Eousseau for the photometric measurements at the Antwerp Exposition. PRINCIPLES OF PHOTOMETRY. 23 It has great advantages. Some experimenters, however, prefer the following method. The quantity of light received by the zone Oi0 2 is equal to ,r A ydO, in which y = /cos 0. We then replace, with sufficient approxi- mation, the above integral by the expression ^ 7" ^ 2 ? supposing y l = Jj cos B l and y 2 = I 2 cos Q. 2 , with the condition that ^ and 2 be sufficiently near one another. Assuming that the angles 1? 2 , O s ,...6 n , are equally spaced, that is, that O l 2 = 2 3 , etc., = A0, the quantity of light received by the total zone Q$ n is given by the expression TT (y, + 2 ?/ 2 + 2y s + - + 2^ + y B )A0. The mean intensity corresponding to this zone is yi + 2y 2 + 2 2/3 + + 2y,_ 1 + y n . fi 2(sin0 n --sin0 1 ) and the mean spherical intensity becomes (2/i 4- 2y 2 + 2y 8 + - 4- 2^ + +0.2588 /oo + 0.2242 /_, + 0.1294 /_,, + 0.0170 J^ In the case of incandescent lamps J.^ is zero.] 24 PHOTOMETRY. > . DC C SI S.2 05 - ^ < o J * *f O 0) H Q. Hi U ho- Q. S < h u o s Q 1 Watts 03 X < v Q. < m a5 rtc t^ 0) CN W * OJ 00 00 10 CN * CM 0) CM o t^ flC rri Q)O O - CM CN OJ * o u +i < N O O O O O rt o > . "\L CD CO < ctf 5 Q) Q. 0) CO CO O CO CO 3 0) 2 o o CO o CO o 1^ M a cj o h- CM O Tf CN O O 10 O CN 2 O ower, 0) ' a 6 o CO 2. TD c o CO 1 CO rt O o CO N 'jZ o O.36O 1 I ; Longitudes North Pole.. Z b CO z o O CO Horizontal . CO b CO CO b CO 1 Q. -M 3 CO Longitudes . a> I z o o (D Z o o CO Horizontal . CO o o CO CO South Pole. CHAPTER II. PHOTOMETERS. 15. Photometers are apparatus by which we may compare the luminous intensities of two given sources of light; they depend on the following principle : making the illuminations, produced on a given surface by the two lights, vary in a continuous and determinate manner until these illuminations are equal. This fundamental principle which is at the base of every pho- tometer is an immediate consequence of the fact (8) that the eye appreciates with maximum precision the equality of the illumina- tions of two surfaces, while the precision with which this organ can determine the ratio of two illuminations is absolutely illusory. The equality of the illuminations which are compared may be obtained in many different ways : A. By the application of the fundamental photometric law, that is by varying the distance or inclination of the surfaces whose illuminations are to be made equal ; B. By methods of diaphragmation and of dispersion ; C. By methods based on the properties of polarized light and by methods of mixture of the lights of the sources that are being compared ; D. By methods based on visual acuteness. The majority of photometers may be included in one of these four categories, although the disposition and construction of the parts, as well as the manner in which the equality of the two illu- minations is determined, vary considerably in different apparatus. E. Besides these photometers those should be mentioned which depend on the various actions of light and which cannot be included in one of the preceding categories. F. There should also be added to the usual photometers intended for the comparison of the total intensity of light-sources, those which are combined with spectrometers in such a manner as to permit photometric comparisons of different regions of the spectra of the two sources to be studied. 2o 26 PHOTOMETRY. A. PHOTOMETERS BASED ON THE FUNDAMENTAL PHOTOMETRIC LAW. 16. We know that the intensity of illumination produced on an element of surface is given by the formula _ /cos i I being the intensity of the luminous source, d the distance from it to the element, i the angle of incidence of the luminous ray on the element. The illumination may be modified by varying the value of d or that of i. If the distance alone is modified, supposing that the luminous rays meet the screen at the same angle of incidence^ photometers are obtained based on the law of the distance. If the distance remains constant and the angle of incidence i alone varies, photometers are obtained based on the law of the inclination. 17. In all photometers based on the law of the distance, the inclination at which the luminous rays of the two sources compared fall on the surface whose illumination is sought, is constant ; it is the distance alone of this surface from the two lights which varies. Consequently the part which is essential and common to all these photometers is one or two divided scales, along which the two lights 'or the screen may be moved. In the majority of cases the arrangement is such that the two lights and screen are along a straight line; the whole is then mounted on an optical bench. Lambert (Rumford) Photometer. 18. This photometer, invented in 1760 and first used by Lambert, bears generally the name of Rumford, because this English physicist used it to such a great extent at the beginning of this century. Let LI and L 2 be the two lights (Fig. 4) whose luminous inten- sities /! and 7 2 are to be compared, T an opaque pencil, and AB a vertical white screen. The light L l projects at L\ a shadow of the pencil T, which is illuminated by the light L 2 only, while the shadow jL'a projected by the latter, is illuminated by L l only. By suitably moving the lights LI and L 2 , we succeed in obtaining the same illumination at L\ and L' 2 ; the eye judges with niceness the moment when this condition is fulfilled. The distances di and d 2 PHOTOMETERS. 27 from LI and L 2 to the screen are then measured, and we have the relation /i = i d* d/ Generally the two lights are moved along a divided scale perpen- dicular to the screen, but sometimes in any manner whatever ; we then neglect the law of inclinations which requires the inclination FIG. 4. Eumford Photometer. to be constant, in order that the law of distances may be exact ; we may take account of this last, and we will find that if L remains fixed, the light L 2 may be moved along a curve whose form might be studied would space permit. But the want of exactness of Rumford's photometer renders this correction deceptive. In practice if we wish to measure rapidly the intensity of a luminous source, say within 10 or 15 per cent, the Eumford pho- tometer is very valuable in that it is easy to set up, but it makes no pretension to giving results which are rigorously exact. Bouguer Photometer. 19. This is the oldest photometer. The screen AB is divided into two equal parts by a partition CC, normal to the illuminated A -dr L 2 -nt FIG. 5. Bouguer Photometer. surface. One of the lights L^ illuminates the half CA of the screen, while the other L 2 illuminates the other half CB-, in order to 28 PHOTOMETRY. establish equality of illumination of the two halves of the screen, the two lights may be moved along divided scales which are per- pendicular to the screen. Most frequently one of the lights, Z/ x for instance, is fixed ; the other alone is movable. The opaque screen is generally replaced by one semi-transparent, say either ground-glass or a sheet of paper; then the equality of illumination of the two halves of the screen is observed by placing oneself on the side opposite the light. Foucault Photometer. 20. The Foucault photometer is only a simple modification of the Bouguer photometer. The partition C does not extend to the screen, but may be moved at will by a special contrivance in such a manner as to reduce to a simple line the shadow which separates the two halves of the screen, one illuminated by L^ and the other by A. To make a reading with the photometer, one of the lights is moved until the illumination of the opalescent screen is as uniform FIG. 6. Foucault Screen. as possible, which is determined by standing behind the screen and looking through the tube T either directly or by the aid of a telescope. The rays from the two lights do not always fall normally on the screen; but care should be taken that they fall invariably at the same angle in order that the factor cos i may be constant. Figure 6 gives a cut of the Foucault screen such as is generally used ; the adjusting screw M serves to move the partition. Figure 7 represents the complete installation of a photometric bench provided with a Foucault screen. PHOTOMETERS. 29 The standard (a carcel lamp) is placed at the right at the dis- tance of one meter ; the light which is being studied is mounted on a piece which is movable along a divided scale ; this movable piece is governed by a crank placed within reach of the observer. Figure 8 represents a sim- plified form of the Foucault pho- tometer, such as the Continental Gas-meter Company of Paris makes. The screen is placed in a box fixed on a support at the front of the apparatus. This form of the Foucault photometer has a disadvan- tage which is relatively con- siderable : it is necessary that the two lights should be placed on the same side of the screen. We may easily over- come this inconvenience by the aid of an arrangement invented by Eitchie (Fig. 9), in which two mirrors m 1? m 2 making an angle with one another throw upon the screen AB the lumi- nous rays coming from the two sources. These mirrors being at right angles, the light which comes from L and.L 2 is reflected normally upon the surface of the screen. Figure 10 shows the details of the photometer employed by Violle in his researches on the absolute standard of light*. The shutters of the pho- tometric box are open at the side to show the interior. * Lum. til., Vol. XXXIV. p. 52. 30 PHOTOMETRY. The side shutters have circular openings for the passage of the rays of light. Two front shutters, of which only one is shown in the figure, keep the light from the two sources from reaching the observer. The screen E is placed at the end of a telescope which allows the observer to verify the equality of illumination of the two divisions of the screen. The two mirrors M and M' are fastened by two plates of metal to the large toothed wheel jR, governed by the crank m, which acts on the rod a and the toothed wheel r. This mechanism serves to turn the mirrors, that is, to substitute the mirror M for the mirror M' and vice versa } in order to eliminate FIG. 8. Foucault Photometer (Simplified Form). the error resulting from differences in the coefficients of absorp- tion and reflection of the two mirrors. In order to effect this movement, it is sufficient to turn the crank m until the wheel R has turned 180 degrees, which is indicated by two stops, one at each end. The figure shows, besides, the construction of the photometric bench, on which the screen is moved by hand by means of a small carriage running along two rails. As the observer determines, by means of the equality of the brightness of the two divisions of the screen, the equality of the PHOTOMETERS. 31 illuminations produced by the two sources of light which are being compared, it is necessary that the two tints should have the same proportion as the illuminations which produce them. FIG. 9. Kitchie's Arrangement. Now the brightness of the screen depends on the coefficients of absorption, of reflection, and of transparency of the opalescent plate. In order that the equality of the brightness of the two halves of the screen may correspond to the equality of the illuminations produced by the two lights, it is necessary that these three coefficients have respectively the same values for the two divisions of the screen ; that is, that the screen be perfectly homogeneous. If this condition is not exactly fulfilled, the resulting error may, however, be eliminated by repeating the measurement after having turned the screen so that the right division becomes the left,, and vice versa. FIG. 10. Foucault Photometer (Violle's Pattern). 21. Construction of the Foucault screen. The nature of the opalescent screen of the Foucault photometer being of very great importance for exactness of measurements, we give some details. 32 PRO TO METE Y. of its construction, taken in great part from a memoir by Crova * on diffusing screens. The information which we give here may be applied also to the construction of diffusers, whose use [as a secondary source of light] plays a quite important rdle in certain photometric apparatus, and to which we shall return later. The screen should be somewhat transparent, but not so much so that the light-source may be distinguished through it ; also the sur- face should be as uniform as possible. Foucault used a screen made of a sheet of plate-glass on which a thin layer of starch or dried milk had been deposited very uniformly; when the layer was dry, it was protected by another sheet of glass fastened at its edges on the first, yet avoiding all contact with it : this result was attained by having previously glued on the second glass a frame formed of narrow strips of paper. The following is the manner in which Deleuil prepares Foucault screens. Wheat-starch is mixed with distilled water, the liquid is passed through a very fine gauze, and after having been allowed to settle for a moment, the milky liquid is decanted and afterwards briskly agitated and poured by means of a pipette upon a sheet of glass laid absolutely horizontal. The glass should have been previously cleaned with the most scrupulous care. When the milky liquid has spread to the edges, it is allowed to stand, then the glass is given a slight inclination by means of one of the leveling-screws of the tripod on which it lies, and the water is drained off by means of a strip of filter-paper acting as a siphon ; finally it is allowed to dry as it lies. The milky liquid should be used immediately, and the temperature should not exceed 18 C. ; experience shows what degree of opaqueness to give the liquid. As to the opaqueness of the layer, it is sufficient to make it of such a thickness that in looking at the sun through the screen we can neither distinguish its outline nor its position. In certain cases screens constructed in this manner are a little too opaque. Crova has succeeded in obtaining them more translucent and of a remarkable homogeneity by employing beet-root starch, whose grains are spherical, of great limpidity, and very small. To obtain this starch we put the grain to soak for several days in water frequently renewed, then each grain is cut in two by means of a very fine scapula ; with a* sharp needle, and making use of a * Ann. de Chim. et de Phys. (6), Vol. VI. p. 342. PHOTOMETERS. 33 magnifying-glass, we detach the little particles of starch contained in the grain, which appear as small white points. This starch is ground in water in a glass mortar, and the milky liquid passed through very line muslin. This method of preparation is very long, but it gives screens of remarkable fineness and uni- formity of grain. Ground-glass may also be used, but it is very difficult to regulate its degree of opaqueness and to give it the necessary uniformity. This surface is also extremely changeable and of remarkable insta- bility ; the least friction, or even slight contact with an organic surface, is sufficient to produce a local change in opaqueness which it is impossible to remedy ; also when a ground-glass satisfying the desired conditions has been obtained, it is necessary, as for the Foucault screen, to protect it in a positive manner by a transparent sheet of glass fastened at its edges without touching it. Some have succeeded in obtaining opal glasses, very homogeneous, of a milky appearance, without an appreciable grain, that have parallel faces ; but these screens modify by a phenomenon of diffraction the tint of the incident light, and that which they diffuse appears slightly reddish. This alteration of the tint by opal glasses offers no inconvenience if the screen is employed simply to determine the equality of illu- minations; but it becomes an obstacle when the screen serves to weaken the light. Relief-Photometers. 22. In the preceding photometers the two divisions of the screen are placed in the same plane. In order that the two sources of light that are compared may be placed along the axis of the same photometric bench, on the two sides of the screen, it is necessary to have recourse to the system of mirrors invented by Ritchie. It is possible, however, to obtain the same result in the follow- ing manner, proposed at first by Villarceau and afterwards adopted with a slight modification by Sylvanus P. Thompson and Starling. In the relief-photometer of Villarceau, the Screen is formed by two opaque plates, p 1 and p 2 , placed vertically on the optical bench and making between them a right angle (Fig. 11). The plate p l is illuminated by the rays of light coming from LI only, while the plate p 2 receives the rays from L 2 only. The equality of illumi- nation of the two faces of the screen may be determined with OF r rr"Kr 34 PHOTOMETRY. the greatest facility ; for the whole screen then appears as a single, plane, illuminated surface, in which the edge of the diedral angle of the screen is no longer perceptible. The luminous intensities of FIG. 11. Relief-Photometer. the two lights are then in the direct ratio of the squares of their distances from the edge of the screen. Conroy* has modified the arrangement of the screens of the relief-photometer of Villarceau, so as to increase the precision of the measurements by removing the difficulty that there was in making the edges of the two divisions disappear. The following is the arrangement invented by Conroyj the details of which are given in Fig. 12. The box inclosing the two screens is placed on the photometric bench in such a manner that the light coming from the light-centers ^^fi , / to be compared enters by the circular open- V f ings A and A'. The screens e and e' are fixed \7 at the extremities of the hypothenusal faces of the two triangular prisms shown; they are simply cut out of a sheet of paper which is white and slightly glazed. The observer looks through the opening and determines the moment when the two screens e and e', being equally illuminated, appear as a single surface. Conroy found that it was advantageous in the measurements to observe the screens at an angle of incidence of about 60 degrees, they being illuminated at an angle of 30 degrees ; these conditions are real- ized in the figure. / \ E FIG. 12. Conroy Screen. \ B 23. In the apparatus of Thomp- son and Starling (Fig. 13) the cunei- form screen is arranged so that the edge a is horizontal ; this arrange- ment requires the observer to verify - Thompson-starim* screen. the equality of the illuminations by placing himself above the * Phil. Mag. (5), 1883, Vol. XV. p. 425. PHOTOMETERS. 35 screen, that is, between the two lights. If it is desired to avoid this condition, it is possible to have recourse to a mirror inclined at 45 degrees with the horizontal, and throwing forward the image of the screen. Bimseii Photometer. 24. Of all the industrial photometers, that of Bunsen is certainly the one that is employed most frequently, particularly in Germany. This is because its manipulation is quite rapid and its indications relatively very precise. Bunsen' s photometer is based on the following property : a spot of oil or grease on a sheet of paper appears bright against a dark FIG. 14. Bunsen Photometer. background, when we see it by transmitted light, and dark against a light background, when we see it by reflected light. Consequently if the paper is equally illuminated on both sides, the spot should neither be bright on a dark background nor dark on a bright back- ground ; it should then disappear completely. The construction of Bunsen's photometer is very easily under- stood (Fig. 14) . The screen E and its accessories are mounted on a carriage movable on a divided bench (an optical bench), on which 36 PHOTOMETRY. FIG. 15. Eudorffs Mirror. are placed at A and B the two sources of light LI and L 2 whose intensities are to be compared. The screen is so arranged that the rays coming from the two lights % v /ft are perpendicular to it. 25. In order that we may ob- serve simultaneously the two sides of the screen, a system of mir- rors, proposed by Kudorff*, is fre- quently employed (Fig. 15). In this arrangement the screen p constitutes the bisecting plane of the angle, 140, formed by the two mirrors Si and S 2 . The screen is illuminated by the rays a and b. coming from the lights that" are being compared. The observer places his eye at o, and sees, through the opening which is left in the side of the photometer, the two faces of the screen reflected at pili and p^ 2 by the mirrors Si and S 2 . The gravest defect of this arrangement comes from the fact that the two images of the spot, j^ andp 2 Z 2 , are too far from one another and are separated by the shadows ra^ and ml 2 ; it is impossible to avoid this inconvenience, since it is necessary that the spot should be at a sufficiently great distance from the edge of the mirror to be always outside the obscure zone ml. Von Hefner Alteneck t has modified Rudorff's arrangement and replaced it by that of Fig. 16, in which the mirrors are replaced by a prism nml placed be- fore the screen rap; the images are contiguous and 110 zone of shadows interferes with the observations. Kruss $ has modified this arrangement so as to avoid the defor- mation of the images produced by reflection and refraction in the prism. * Journal fur Gasbeleuchtung, 1869, p. 567. t Elektr. Zeitschr., 1883 ; Lum. Jfo, Vol. X. p. 500. t Centralblatt fur Elektr., Vol. VI. p. 781. FIG. 16. Hefner Prism. PHOTOMETERS. 37 Figure 17 gives the details of his modification. The screen P is placed in the median plane of the two prisms / and 77. The angle formed by the faces of these prisms is so chosen that the rays which fall perpendicularly on the face A t of the prism /, and which come from the points ab of the screen, are reflected at B l} C^ and A 19 and emerge from the prism perpendicularly to the face D lt The rays follow an analogous trajectory in the prism II. A tube of variable length to suit the observer may be placed before the faces D l and D 2 ; this tube is terminated by a diaphragm of small opening which fixes the position of the eye in the plane of the screen. FIG. 17. Kriiss Prism. The eye then sees the visual field divided into halves by the line of separation a of the two faces DI and D 2 ; at the right is found the image of the right side of the screen illuminated by one of the lights LI. The image of the left side of the screen illuminated by the other light L 2 is found at the left. The image of a thus falls in the zone a, and that of b in the lateral parts of the visual field (3i and /? 2 . If the part ac of the screen represents the spot, y x and y 2 repre- sent the images of the edges of the spot, and the comparisons are exact. A Bunsen screen may be transformed immediately into a Foucault screen by suppressing the spot or removing it outside of the field of vision. 38 PHOTOMETRY. The nature of the paper which constitutes the screen and that of the spot have a considerable influence on the precision of the measurements. In order to take account of them in an exact manner, a complete theoretical study of the apparatus should be made. Theory of the Bunsen Screen*. 26. Let us consider the most general case in which the two faces of the screen are not identical, that is, they have different coefficients of transparency and reflection. We may afterwards simplify the formula by assuming the identity of the two faces. Let us designate by % the coefficient of absorption, by ^ the coefficient of transparency, by r the coefficient of reflection of the opaque part of the left face of the screen, and by a/, /, r/, the same coefficients relative to the left face of the spot. Let us desig- nate in the same way by 2 , t 2l r 2 , and a 2 f , t 2 , r 2 ', the same coefficients relative to the right face of the screen. The coefficient r^ for instance, determines the illumination of the opaque part of the left face of the screen due to the light L { at the left, while t v determines the illumination of the same part of the screen due to the light L 2 at the right ; the other coefficients determine in the same way the illumination of the other parts of the screen. These coefficients vary with the direction from which the ob- server looks at the screen. Assuming that the screen satisfies the law of Lambert, we should have a + 1 + r = 1. It may practically be assumed that this law is satisfied, on con- dition that the screen is always observed from the same direction. Let 6i be the intensity of illumination of the left side of the opaque part of the screen, and let e/ be the intensity of illumination of the left side of the spot ; designate by e 2 and e 2 the corresponding quantities relative to the right side of the screen. Further, let /! and 7 2 De the intensities of the lights at the left and the right, rfi and d 2 their distances from the screen ; we obtain immediately, neglecting a factor in the final result, * Leonard Weber, ThSorie du Photometre de Bunsen; Wiedemanns Ann., Vol. XXXI. p. 676 ; Lum. til., Vol. XXXI. p. 267 ; Boulouch, Sur le photo- metre de Bunsen, Comptes Rendus, Vol. CV. PHOTOMETERS. 39 2 ~ d, 2 d? There are, then, on each face of the screen two intensities of illumination, viz. e l and e-f on the left face, and e. 2 and e 2 ' on the right face. Observations may then be ma:le in three different ways, viz. : 1. The two illuminations e l and e/ are made equal, that is, the spot disappears on the left face of the screen ; 2. The two illuminations e 2 and ej are made equal, which cor- responds to the disappearance of the spot on the right side of the screen ; e ' 6)' 3. The ratios and are made equal, that is, the spot stands e l 2-2 out from the rest of the sheet of paper with the same intensity on both sides of the screen. Suppose the two lights fixed and the screen movable ; call L the position of the screen corresponding to the first method of observa- tion, R the position corresponding to the second method, M the position corresponding to the third method of measurement. The point M is generally situated between L and R. As to the relative positions of L and R, two cases are distinguished accord- ing to the nature of the screen. In the first case, the point L is situated at the right of M, and the point R at the left; these three points then succeed one another in the following order : R, M, L going from left to right ; th screen is then called & negative screen; if the three points succeed one another in the inverse order, it is called a positive screen. The sign of the screen depends upon the coefficients of trans- parency and reflection of the spot and of the opaque paper adjacent. With a positive screen a case may be presented where the three points L, M, R coincide. The spot appears bright on a dark back- ground in the position M ; it is dark on a bright background with a negative screen. [See Appendix A.] These two distinctive characteristics obtain only when the spot is more transparent than the rest of the screen; they should be inverted when it is less transparent, which takes place, for instance, when/ it is formed by an opaque varnish. 40 PHOTOMETRY. If the screen is managed in such a manner as to make the spot on the left face of the screen disappear (position L), we have e l = e ; that is, M JA_W #/ <*i 2 d- 2 "" di 2 rf 2 2 Whence, / 1= ^-^^ / 2 . Cn-r^ctf , 9 Designate by p the ratio _L, and we have Observing the disappearance of the spot on the right side in the same manner (position R), we have If we assume that the coefficients are in equal pairs, that is, r 1 = r a , ^ = 2, ?Y = r 2 ', tj = tj, we obtain, taking the product of the two preceding relations, J 1= V^ip 2 / 2 . (3) This formula supposes that the two faces of the screen are identical ; we may free ourselves from this restriction by making two new settings p z and p 4 , having turned the screen around. We have then (4) An analogous result is obtained by employing the third method, in which the observations are made in the position M : such a point is chosen as to obtain equal contrasts of illumination, that is, we make ^ = e A. ei e 2 The ratio of the illuminations, and not their difference, is con- sidered since, from the psycho-physical law of E. H. Weber (8), the perception of the differences of two sensations is proportional to their ratio, and not to their difference. PHOTOMETERS. 41 We have then e 2 The condition !L = ?I e l e 2 gives, then, for I L the quadratic equation KJ? + Pl (K 3 - JBT 4 ) JjA + ^prt 2 = 0, in which Assuming the identity of the two sides of the screen, we have K z = K and K = -fiT 2 ; the ordinary formula is then obtained, /i = A4 (5) In the general case the coefficients r and may be eliminated by taking a second setting p 2 at ^ after having turned the screen. The factors K^ and K^ and ^T 3 and K are then inverted, and we obtain 27. To complete this brief theory of the Bunsen photometer, it is necessary to deduce in addition the formulae for calculating errors of measurement. The error A/ x of the result depends on the error Ap of the setting p'j the following considerations give the algebraic expression of this dependence. In the case where one is limited to a single measurement (formula 2), In the case where two settings p 1 and p z are made, it may be assumed that the errors &p 1 and Ap 2 are equal. We then have (formula 3 or 6) M = i V 2^. (3' and 6') 42 PHOTOMETRY. Finally, if four settings have been made, we have It is necessary then to evaluate first of all the ratio -^-. p This ratio depends on two factors which vary according to the nature of the observation (L, R, M). The first is a function of the coefficients r and t, that is, a function of the nature of the screen; the second factor depends on the psycho-physiological qualities of the eye, and in particular on the faculty, more or less great, of the eye to perceive the equality of illumination of two- surfaces (at R or L), or to perceive the equality of the contrasts of two illuminations. , Designate by A^! - the ratios of the illuminations or of the contrasts still perceptible to the eye at the limit ; there will be found after many reductions the following values for the ratio -^, in the three principal positions of the screen: p The constants f ly / 2 , F, have the following values fi= ^ + A' + i t.' + r,' ^ PHOTOMETERS. 43 For simplicity it has been supposed, in the calculation of JFonly, that the two sides of the screen are identical. The factors f lt f 2 , and F are the coefficients of sensibility of the screen for the positions L, R, and M. The minimum value of /! or / 2 is equal to 1, while that of F is equal to 0.5. However, these coefficients have values in reality much higher. Construction of the Bunsen Screen. 28. In the construction of the Bunsen screen the coefficients of sensibility f l9 / 2 , and F should be made as small as possible. For -this it is necessary that the coefficients r/ and ^ should be very small, r x and / being very great. The best screen is therefore made from a dull, white, opaque disc, while the spot should be as transparent as possible, and affected by an insensible coefficient of reflection. The error of the measurements depends also on the sensible values of the perception, Ag : , Ag 2 , and AQ. Now these sensible values become less in proportion as the delimitations of the spot and of the opaque part of the screen become more perfect. With certain screens we may have favorable values for the coefficients of sensibility / and F, but unfavorable values for the sensible values A# and AQ. With regard to this, the following numbers obtained by Leonard Weber of Breslau, with eight different screens, allow an exact idea of the size of these coefficients to be formed. These eight screens, designated by the figures 1 to 8, have considerably different co- efficients, which is furthermore a consequence of the differences in their construction, which the following description takes into account : 1. Toepler Screen: A sheet of white paper pierced with a circular hole, covered on each side with a sheet of tracing-paper and put together without glue. 2. Two thin pieces of white cardboard pierced with a circular hole, and between them a sheet of tracing-paper. 3. and 4. Kruss Screens: Sheets of white school-paper with a paraffine spot. 5. White cardboard pierced with a hole, covered with a sheet of tracing-paper blackened with plumbago so as to have unequal faces. 44 .PHOTOMETRY. 6. Two sheets of white paper exactly alike, pierced with a hole, and covered on each side with a sheet of tracing-paper. 7. Two sheets of white paper, between which is a sheet of tracing-paper. 8. Oiled paper, the spot being formed on each side by a band of white varnish. The following table includes values obtained for the ratios of the coefficients r and t of the left face of the screen ; with the exception of number 5, the differences between the two faces are insensible. The sixth column includes the mean of the values of / x and / 2 , which, moreover, differ slightly; the seventh includes the mean of the corresponding values A^ and Ag 2 ; that is, The last two columns include the values of F and AQ. Number of the screen. 3 V *i *i A' ri' / A? F A r whence r-n In the second method, the lights LI and L 2 are placed at right angles with reference to the edge of the photometer ; but this arrangement has certain inconveniences. However, we shall not dwell longer on this apparatus, which is very carefully planned, but which does not give results sufficiently exact in all cases. B. PHOTOMETERS BASED ON THE EMPLOYMENT OF DIAPHRAGMS AND DIVERGING LENSES. 33. In photometers of the first category, the equality of bright- ness of the two halves of the screen is obtained by varying the distances of the lights from the screen, or the inclination of the luminous rays on it. In photometers of the second category, the equality of brightness is obtained by various methods, which diminish the luminous inten- sity in a well-determined ratio. Among these, special attention should be paid to methods of diaphragmation, dispersion, and those which are based on the phenomena of absorption. Before entering on the special study of these methods, let us first make a brief exposition of their theory. Theory and Properties of Diaphragms. 34. Let us consider the illumination produced on the wall of a dark room by light coming from outside, and passing through [a translucent diaphragm placed behind] an aperture in the opposite PHOTOMETERS. 53 wall ; if the rays of the luminous pencil are parallel, the wall will be uniformly illuminated. But if the aperture is diminished one- half, the quantity of light received on the opposite side will also be diminished in the same ratio ; in general, the quantity of light received by the wall which serves as a screen will be directly pro- portional to the size of the aperture. Let /! be the intensity of a source of light L placed normally to, and at a distance D l from the diaphragm; the intensity of illumination of this last is then -=^, and the quantity of light */i received by the surface of the diaphragm, being proportional to its T 0< area S^ is then equal to -^ L - This surface acts in turn as a MI source of light; and at a distance di from the diaphragm, the illumination produced by the illuminating surface S t on a surface S normal to the rays of light is equal to % is a factor of proportionality, which depends on phenomena of reflection, refraction, and diffusion, of which the screen is the seat. This intensity of illumination may then be varied by varying the surface Si of the diaphragm. The second source of light L 2 being in the, same way placed at the distance D 2 from a second diaphragm S% the intensity of illumi- nation e 2 produced by this last on the surface S, normal to the rays of light coming from L 2 and situated at a distance d 2 from the dia- phragm, is equal to LS. 2 '**Dfdf' If the factors j and a 2 are known, the ratio of Jj to J 2 may be immediately determined by measuring the surface Si and S 2 of the two diaphragms at the moment when the above equation is satisfied. Instead of measuring the coefficients ^ and 2 , which are more- over hardly constants, it is simpler to eliminate them by combining the measurements in a special manner. This result is easily reached by employing an auxiliary light L , on whose constancy we may rely. The intensity of illumination produced on the screen S by the rays of light from L is given by the relation 54 PHOTOMETRY. in which J represents the luminous intensity of L , S the area of the diaphragm, D its distance from L 0) and d its distance from the screen. Illuminating the screen simultaneously by the lights L and L lt we succeed in equalizing the illuminations e ( = /iTo/o^o) and e^ ( = KiIiSJ ; we have then (1) The coefficients K and Tfi have the following values : o AW Next the light Z/ 2 is substituted for the light LI, and equality of the two corresponding illuminations eJ(=K t IA t ) and e., ( = A'i/A) is established by varying the opening of the diaphragms, th.it is, EMSJ = KJJ8* (2) The factors K are the same as in the preceding observation since the arrangement of the apparatus has undergone no modifi- cation. Dividing these two equations member by member, we obtain whence = - < 3 > 2 In the majority of cases, the diaphragm interposed in the path of the rays of light from LI and from Z/ 2 may be suppressed ; in this case equation (3) becomes simply J"<0/ The Properties of Dispersion Lenses. 35. Let us suppose that a double-concave lens be placed at a distance p (Fig. 24) from the source of light L and that a screen be placed at a further distance 8. The distance of the screen from PHOTOMETERS. 55 the source of light is then p -f 8. The divergence of the luminous pencil proceeding from L is increased, on passing through the lens, in such a manner that the rays of light seem to come from the virtual focus L', situated at a distance p' from the optical center of the lens. FIG. 24. The photometric screen being placed perpendicular to the optical axis of the lens, the refracted pencil of light then illuminates a circle of radius r'(= AB'), while the original pencil would only have been distributed on a circle of radius r(AB). Neglecting the correction arising from the fact that the screen is plain and not spherical, a correction furthermore negligible if observations are made near the axis, the intensities of illumination obtained in the two cases are inversely proportional to r 2 and r f2 ; now L and L' are conjugate foci; and calling/ the focal distance of the lens, we have, applying the fundamental equation of diverging lenses, and p f pf P+f The radius of the lens being equal to p, we have and whence P P 56 PHO TONETE T. and we obtain, after making certain reductions, ^1-1 Consequently the intensities of the illuminations produced with and without the interposition of the lens in the path of the rays of light are to one another in the ratio JV: In other words, the illumination produced on a screen by the source of light is the same as if its distance had been increased in the ratio : we must then introduce into the calculation, in place r of the distance d (=p + 8), the distance d' expressed by the relation or The above formula may also be put in another form ; now =d 8 hence In this equation the modified distance is expressed as a function of the real distance, of the constant / of the lens, and of the dis- tance 8 of the lens from the screen. Putting ch = 1 + i S 2 and a 2 = - , we have d'= a^d a^. 36. We may then calculate in advance the various values of ai and a 2 for a given lens and for various values of 8. PHOTOMETERS. 57 The weakening effect of the lens is null when the bisecting plane of the lens coincides with the screen, that is, when 8 = 0; it is also null if p = 0, that is, if the source of light is at the optical center of the lens. The weakening effect is maximum for an intermediate position determined by equating to the derivative of d' with respect to 8. We obtain then 8 = -, whence we conclude that the maximum dispersive effect is produced when the lens is placed at equal dis- tances from the light and the screen. In the above calculation, 110 account has been taken of the weakening of the rays of light due to absorption and reflection produced by the lens. At first sight we might assume that these causes of weakening are insensible, considering the slight thickness of a diverging lens, especially near its center. Aryton and Perry have done this in making formulae for their dispersion-photometer. However, precise measurements made since allow the conclusion that the weakening action due to reflection and absorption by the lens frequently attains a value of from five to eight per cent. It may be determined, furthermore, that the weakening of the pencil of light, caused by the lens, comes entirely from phenomena of reflection, and not at all from phenomena of absorption ; the weakening is, in fact, the same with plates of glass of different thickness as with lenses. Below will be found the ratios of the illuminations observed on the screen by Voller*, and obtained with and without the lens, for various lights ; the results obtained with plates of glass of various thickness complete the table. Lens. Lens. Plates of Glass of a Th ickness of /=18cm. /=50cm. 1.0 mm. 2.9 mm. 4.8 mm. andle Petroleum lamp . . . Gas-burner 0.966 0.933 0.923 0.914 0.902 0.916 0.918 0.923 0.910 0.910 Incandescent lamp 937 900 The result of these measurements shows, then, that we should determine experimentally the weakening factor of a given lens * Abhandl, des Naturwiss. ver. zu Hamburg (7), Vol. II. p. 40. 58 PHO TOMETE Y. before employing it in photometric comparisons ; we may, however, eliminate this reduction by compensating the weakening action of the lens by inserting in the path of the rays of light from the photometric standard plates of equivalent thickness. Cornu's Method. 37. This method* is based on the following property of con- verging lenses, discovered and already used by Bouguer : if with a, converging lens a real image of a luminous source is formed, and the aperture of the objective is modified by inserting a diaphragm of greater or less opening, the size and position of the image are not modified; on the contrary, the intensity of illumination of the image is proportional to the opening of the diaphragm, provided that this opening is always small with respect to its distance from the light. This last property is evident, since the quantity of light which contributes to the formation of the image is proportional to the surface of the lens, met by the incident rays. For a diaphragm, Cornu made use of the following arrangement known as a cat's eye. It is formed by two metallic plates each with a square opening, AB and A'B', made to glide on one another by a pinion working in two racks C, C" (Fig. 25). In one of their extreme positions the two squares are in coinci- dence, and a maximum square opening allows the passage of the light; in the other extreme posi- tion, the opening of one of the plates is covered by the solid part j \' > rlc' of the other so that no light may pass; in the intermediate posi- tions, the free opening has the form of a square, whatever its. dimensions. Further, since the pinion is fixed, and its rotation makes one of the plates advance as much as the other recedes, the center of the variable square remains fixed in front of the optical center of the lens. Consequently, the opening is always proportional to the square of the displacement of the movable plates the diagonal of the opening measured on the graduated scale of the apparatus. The most simple means of utilizing this method consists in * Journal de Physique, Vol. X., 1831, p. 189; Lum. El., Vol. III. p. 221. PHOTOMETERS. 59 employing two identical objectives, fitted with these diaphragms and so placed that their optical axes cross at about twice their com- mon focal lengths. Each of them produces, on a white screen, the image of a small opening in another diaphragm in front of that part of each of the lights which it is desired to compare. The diaphragm of the lens in front of the smaller light being open to its fullest extent, the opening of the other is regulated until equality of illumination of the two images is obtained. To better determine this moment, the apparatus is so managed that the images of the openings of the small diaphragms are in con- tact along one of their edges; this edge disappears then at the moment of equality. This apparatus permits an easy measurement of the intrinsic intensity of a light at various points, by employing an auxiliary light. Cornu has given his apparatus another form which is more prac- tical and more general, and which does away with the screen. The iintinned mirror* is replaced by a mirror of black glass AA (Fig. 26), ending in a rectilinear edge A normal to the plane of the principal axes of the objective. The focal planes are so regulated as to pass exactly through this edge. 1 A microscope of small magnify- ing power allows one to see the images of the two sources simulta- neously, on each side of the recti- h linear edge. By suitably regulat- A ing the position of the lights, the two regions to be compared are brought into contact at the edge. To render the comparison still more A b C' exact, the two regions are isolated by the aid of a circular diaphragm CO 1 introduced in the focal plane FIG. 26.- Cornu's Arrangement. of the eye-piece of the microscope. The visible field consists then of a small circle divided into halves by the almost invisible line formed by the edge; one of the halves has a fixed intensity, the other an intensity which is rendered variable by the aid of the pho- tometric screen : these are the best conditions for obtaining equality of the two intensities. Under these circumstances, and above all if * Journal de Physique, Vol. X., 1881, p. 192. 60 PHOTOMETRY. care is taken to diminish the intensities to a certain limit, the eye acquires so great sensitiveness that the least difference in the com- position of the lights betrays itself by a difference of tint which becomes troublesome in appreciating their equality ; it is only lights which are strictly identical or monochromatic which give an abso- lutely satisfactory impression of equality. The surfaces to be compared may be extremely small ; if the focal images are quite pure and obtained by the aid of achromatic objec- tives, the microscope which serves as an eye-piece may greatly mag- nify them ; the apparatus then is able to measure the brightness of extremely small images. The above apparatus gives only the intrinsic brilliancy of the different regions of the lights which are studied. To compare the total intensities, we should use diffusing screens on which the rays of the lights to be studied fall, and which are placed immediately before the diaphragms of the two lenses. Napoli's Photometer. 38. This photometer* puts into practice in a very ingenious manner the principles of diaphragmation. Suppose a disc pierced with a hole at any distance from the cen- ter, and a light placed before this hole ; if the disc is turned, the image is displaced circularly on the disc, and forms, by the per- sistence of the image on the retina, a uniformly illuminated ring. The brightness of this ring is independent of the velocity of the disc, and depends only on the surface of the opening, that is, on the sur- face of the diaphragm. The ring will then be more or less bright according as the surface of the opening is increased or decreased, and the intensity of brightness will be proportional to the size of the opening. Figure 27 represents the principal part of the photometer, namely, two peripherally notched discs D and D', of the same diameter, in juxtaposition; they move on one another in such a way as to present spaces either open or more or less filled at the will of the observer. One of these discs D is fixed to an axis set rotating by a crank, a fly-wheel, and an endless cord. The second disc D' is movable on the axis of the disc D, and carries a cylinder with a helicoidal slot, in which a pin held by the * Seances de la Soc. de Phys., 1880, p. 53 ; Lum. El., Vol. II. p. 133. PHOTOMETERS. 61 sleeve C engages ; this sleeve, by means of a key, may move longi- tudinally in a second slot made in the axis of the disc Z), and fol- lowing a generatrix. It ends in circular teeth and is operated by the button B and the pinion P. Turning the button _B, the teeth advance or recede, and the disc D moves on D' ; the pitch of the slot is so calculated that, for the whole course of the sleeve, the two discs may pass from a position completely intercepting the light to one where all the slots are open. A pointer fixed at B on the axis of the pinion indicates on a dial the opening of the slots. FIG. 27. The apparatus is mounted in connection with a Foucault screen ; one-half is illuminated by a standard light, the other by the light to be studied, reduced in the ratio indicated by the pointer of the apparatus. It is sufficient to move the button B until the two divisions of the screen are equally bright. It may be mentioned that the same principle was applied to the construction of photometers, at about the same time, by Guthrie * in England and Hammerl f in Germany. Ayrton and Perry's Dispersion Photometer. 39. This photometer $ is based on the properties of diverging lenses. Equality of illumination is determined by Eumford's method. * Chem. News, Vol. XLIX. p. 202. t Elektr. Zeitschrift, Vol. IV. p. 262. t Phil. May. (5), Vol. IX. p. 117. 62 PHOTOMETRY. The opaque body, the equality of whose shadows is determined, is a rod placed in front of a sheet of white paper ; the photometric standard is movable along a graduated scale. The light to be studied (electric lamp) throws its rays upon a plane mirror, which reflects them upon a concave lens ; this disperses them and reduces the illumination produced in an easily calculated ratio, so as to obtain equality of the two illuminations without moving the light. The mirror makes an angle of 45 with its axis of rotation which is perpendicular to the disc and parallel to the axis of the lens ; hence all the rays reflected by the mirror and passing through the center of the lens have the same angle of incidence, 45, and thus undergo the same absorption, whatever be the position of the light with respect to the mirror. Further, the particular value of this angle, 45, is such that the angle through which the disc must be turned to reflect a pencil of light first horizontal, then inclined, gives immediately this inclina- tion. The whole apparatus may turn about an axis so that the pencil reflected by the mirror and refracted by the lens is projected upon the middle of the screen. As to the luminous intensity / of the light studied, adopting as a unit the light employed, and applying the formulae for dispersion lenses, we obtain in which / is the focal length of the lens ; r the horizontal distance from the light to the mirror ; / the distance from the mirror to the screen ; the angle of elevation of the light, or the inclination of its pencil of rays directed toward the mirror ; x the quantity x = r' -h r sec 6 ; 8 the distance from the lens to the screen ; 8' the distance from the photometric standard at the time when the shadows are equal. To the results thus obtained, we should apply the correction which takes account of the loss due to reflection on the surfaces of the lens. PRO TOMETER S. 63 Crova's Method. 40. Crova's method* is a method of diaphragmation combined with the employment of a diffuser on which the light from the sources to be compared falls. On a sheet of ground glass, opal glass, or a Foucault screen, are let fall normally, the rays emitted either by the light to be meas- ured LI, or by the standard light L 2 - Every point of the back of the diffuser may be considered a source which emits light whose intensity depends on the nature of the diffuser; but whatever be this law, the rays diffused in a nearly normal direction have a uniform intensity if the screen is homo- geneous, whatever be the point from which they emanate. We place, then, behind the diffuser, an opaque screen having a slit whose size may be varied at will. The intensity of illumination at a point of the screen is then proportional to the surface of the diffuser. Varying the surface of the latter by means of the variable slot in the diaphragm, we may make this illumination equal to that of another part of the same screen, illuminated by a constant auxil- iary light. When lights of very different intensities are compared, it is necessary to place them at different distances from the diffuser; for if the distance were the same for the two lights, it would be necessary, in the case of the intense light, to give to the opening of the diaphragm a very small surface, which might bring about phenomena of diffraction. This necessity of placing the two lights at different distances D l and D 2 from the diffuser does not compli- cate the method ; Si and $ 2 representing the area of the opening of the diaphragm in the two cases, we have This method has given good results, in the comparison of arc- lights for instance. The apparatus used by Crova is composed of a vertical Foucault screen, one-half of which is lighted by a Carcel lamp, which serves as an intermediate standard. This lamp is placed in a blackened box, fitted with a large horizontal tube 50 cm. in length, also blackened inside, which allows the light to fall on the screen at an angle of 45. * Comtes Eendus, Vol. XCIX. p. 1067. 64 PHOTOMETRY. The other half of the Foucault screen receives the light from the diffuser, which is placed at the end of a horizontal tube of the same length as the preceding to which it is perpendicular; in this way the two parts of the screen receive light at the same angle, 45. As has been said, immediately behind the diffuser is found the diaphragm, whose aperture may be varied by means of a micrometer screw. Finally the board on which the photometer is fixed may turn about a vertical axis, so as to allow the tube carrying the diffuser to be placed in all azimuths. The apparatus invented by Crova also permits the measurement of the luminous intensities in any direction. To accomplish this, the tube at the end of which the diffuser is placed may be moved in a vertical plane, perpendicular to the axis of the tube containing the lamp. A divided circle fixed on this last tube allows the angle between the normal to the diffuser and the horizontal to be read;. the value of this angle permits the calculation of the ratio of the intensities / x and /,. Let us suppose, to measure / 1? that the diffuser is vertical, while in measuring I 2 its normal makes the angle i with the horizontal \ for a uniform illumination of the screen we shall have A Si cos 45 = A S 2 cos 45 cos i, DI L/t ! 2 whence ~ = g * cos i. J.% Oj-L^j It should be remarked that the diffusion photometer of Crova supposes a perfect diffuser; for the construction of the latter, let us refer to the details that we have given concerning the construc- tion of the Foucault screen ( 21). An essential condition of Crova's photometer is, furthermore, the necessity of choosing dif- fuse rs whose opaqueness varies with the intensity of the lights to- be compared. Mascart's Photometer. 41. This apparatus * uses at the same time diffusers and lenses provided with diaphragms; it allows the comparison of lights of very different intensities, and the measurement of the intensities of rays of light in any direction without measuring the angles. * Bull, de la Soc. int. des tflectriciens, 1888, p. 103; Bull. d. sc. Phys.+ Vol. I. p. 250. PHOTOMETERS. 65 The incident light strikes the Foucault screen Z>, passes through it, and is reflected in a mirror M along the axis of the apparatus (Fig. 28). A lens C placed against the movable diaphragm, and distant from the screen twice its focal length, produces the image of this screen D on the Foucault screen E. From the lamp L, the height of whose flame is regulated by means of its image thrown on the ground glass 6r, proceeds a pencil of light which is concentrated by a lens on the Foucault screen D, of the same dimensions as the first. A lens C placed against the second movable diaphragm, and dis- tant from the screen double its focal length, gives the image of this fl/ O / Sv FIG. 28. Mascart Photometer. screen on E, after having been reflected by the mirror B and the prism A. An adjustable lens at the point F enables us to see clearly the Foucault screen E, on which are projected the two pencils, each of them occupying half of the disc. The effect of the difference of coloring is corrected by means of the diaphragm H, composed of glass of various colors, which permits the equalization of the tints of the lights. Practically, the apparatus is used as follows : After having lighted the small lamp, the height of whose flame is regulated by means of its image in the ground glass, we arrange the apparatus so that the screen D receives normally the light of the standard lamp L^ placed at a meter's distance from this screen. Next we vary the opening of the diaphragms until the illumi- nations of the two halves of the screen E are equal ; these openings being rectangular, their surface is proportional to their breadth n, read directly on a divided scale. The intensity of the auxiliary lamp being /, we have then 66 PHOTOMETRY. We next repeat the same operation with the light L 2 , whose intensity J 2 we wish to measure ; we then have D being the distance of the light L 2 from the diffuser. We then have ** = ?*.& /i Wi'na In Mascart's photometer, as in that of Crova, we have assumed that the quantity of light emitted normally by the diffuser is proportional to its surface and to the quantity of light which it receives. This hypothesis has been confirmed by direct measure- ments by Mascart, and its precision has been established with errors less than three per cent. It follows from this that the ratio W should vary inversely as the square of the distance, since the quantity of light received by the diffuser varies in the same manner. We may then determine this ratio once for all; that is, we may take the intensity of the lamp of the apparatus as an intermediate standard. Beside the preceding apparatus, Mascart has had constructed by Pellin a small apparatus which may be held in the hand, in which the auxiliary light is a small petroleum lamp. Further, the slitted diaphragms are replaced by discs pierced with holes of unequal size ; the illumination of the two parts of the screen E then varies by sudden leaps, but without any resulting inconvenience. Employment of Absorbing Media. 42. We may also equalize the illuminations of the two halves of the photometric screen by placing in the path of the rays of light from one of the two sources that are being compared, media more or less opaque which absorb a part of the light. We may employ with success smoked glass of varying thickness and tint. Before using this glass its absorbing power is carefully deter- mined. To make the illuminations of the two halves of the screen exactly equal, it is necessary to insert suitably chosen glasses. But in proceeding in this way the illuminations do not vary con- tinuously. PHOTOMETERS. 67 To eliminate this inconvenience, Sabine * has proposed employ- ing a single smoked glass cut 011 a bevel, whose absorbing power varies with its thickness. By introducing little by little this wedge in the path of the pencil of light coming from the source to be compared, the illumination of the screen is varied in a continuous manner. The amount which the wedge enters the slot is measured on a divided scale; this gives immediately the corresponding weakening of the pencil of light, determined in advance once for all. Sabine' s photometer includes also a diaphragm whose arrange- ment has nothing novel. The employment of the absorbing wedge has a serious incon- venience. The luminous intensity is not weakened equally in all parts of the section of the luminous pencil, because of the unequal thickness of the wedge. The photometric screen is consequently not uniformly illuminated. Spitta f has overcome this inconvenience by replacing the wedge by two bevelled sheets, with their hypotenusal faces put together. Moving the two wedges on one another, the total thickness varies, but it is constant for a certain length, greater than the size of the luminous pencil. The absorption of this double wedge is determined in advance for the different positions of the two superposed halves. It then suffices to read their position on a divided scale in order to obtain the absorption. This arrangement has not yet been employed in industrial apparatus, but it is ingenious and merits notice, because of the applications to which it is susceptible. The weakening of the rays of light by the absorbing media may give excellent results when the lights compared are of the same tint. If this is not the case, the absorption is not equal for the two lights; there are then produced secondary actions of which it is difficult to take account, and which greatly complicate the measurements. C. POLARIZATION AND COMPENSATION PHOTOMETERS. 43. In the photometers already described, the illumination of the two parts of the screen has been equalized, either by varying the distance or the inclination of the rays, or by interposing in the path of the latter, dispersion lenses, diaphragms, or absorbing media. In addition to these various ways of diminishing the intensity of * Phil Mag. (5), Vol. XV. p. 22. t Proceedings of the Royal Society, London, Vol. XL VII. p. 15, 1889. 68 PHOTOMETRY. a pencil of light, there still exists one, based on the properties of polarized light. Let us recall, in a few words, the properties of polarized light. We know that light is the result of transverse vibrations of the ether. In the case of ordinary light, the vibrations take place in all directions, in a plane perpendicular to the direction of propagation. If a ray of sunlight is passed through a rhombohedron of quartz, it is decomposed into two distinct rays, the ordinary ray and the extraordinary ray. These rays are said to be polarized. The un- dulations of the ether are produced always normally to the direction of propagation of the wave, but they take place for each ray in a single direction, instead of in all directions. In the ordinary ray the undulations take place in a plane perpen- dicular to the plane determined by the incident ray and the normal to the surface of the crystal. In the extraordinary ray the undula- tions take place in the plane of the incident ray and the normal to the surface of the crystal. A ray of natural light may then be considered as constituted of two independent rays, whose intensity is equal to one-half of that of the natural ray, and which are polarized in planes perpendicular and parallel to the plane of incidence. We know that the analyzer of a Nicol prism is formed of a rhombohedron of Iceland spar cut in two along a plane perpendicular to the plane of the principal diagonals of the bases and passing through the obtuse angles which are nearest one another ; the two halves are afterward cemented together with Canada balsam, whose index of refraction is smaller than the extraordinary index of Iceland spar, but greater than the ordinary index. Consequently the ordi- nary ray undergoes total reflection at the surface of separation, so that the prism allows only the extraordinary ray to pass. If this polarized ray is received on a second Mcol prism, whose principal section makes with that of the first an angle a, the lumi- nous intensity /' of the ray which emerges from the second Nicol prism is related to that of the ray which emerges from the first by the law of Malus : Varying the angle a from 90 to 0, we may vary /' from to / in a well-determined manner. We have thus a precise process for varying the luminous intensity of a given pencil of light previously polarized. PHOTOMETERS. 69 Duboscq's Photometer. 44. Polarization photometers are based on this principle. The first in date is that of Arago *, based on a property of polarized light which he had just discovered ; viz. when a pencil of natural light falls on a pile of plates of glass, the quan- tity of light polarized by reflection is equal to that polarized by refraction. Duboscqf has constructed a piece of apparatus based on the same principle and which has been wrongly attributed to Babinet. Below is the description of the apparatus (Fig. 29). The lights />, and L 2 are placed behind sheets of ground glass; the rays which they emit meet a pile of plates of glass P, which reflects the light coining from L and refracts that coining from L 2 in the direction of the eye. These lights are partially polarized in rectangular azimuths ; if their intensi- ties are equal, the quantities of polarized light which they contain will produce nat- ural light. We determine the absence of polarization by the aid of Savart's polariscope, composed of the double rotation plate Q and the analyzer N. The distance of the unknown light L 2 is varied until this result is attuned. We then have, designating by di and d. 2 the distances of the lights from the diaphragms, and by J x and J 2 their intensities, FIG. 29. Duboscq's Photometer. Wild's Polarization Photometer. 45. Wild's polarization photometer $ is the only one which has been especially contrived for industrial measurements. The first form of this photometer dates from 1859, but Wild later on woiked out an industrial form which was constructed by Pfister of Berne . * Comptes Rendus, Vol. XIII. pp. 840, 967. t Cours de Physique, par Jamin et Bouty, Vol. III. fasc. 3, p. 579. } Poggendorfs Annalen, Vol. XCIX. p. 235 ; Vol. CXVIIL p. 193. Melanges physiques de Saint Petersbourg, Vol. XII. ; Bull, des sc. phys., Vol. I. p. 578. 70 PHOTOMETRY. The lights to be compared, S and S', are placed in the direction of the axes of the tubes A and B (Fig. 30), which make between them an angle of 70 50', twice the complement of Brewster's angle (54 35'). The pencils of light emitted by each of them pass through the diffusers of opal glass D, D, then through the Nicol polarizers P, P, fixed on the divided circles (7, C, which may be turned before the fixed verniers by means of the rods &, 6. They next meet a pile of plates of glass G, G, directed along the bisector of the angle formed by the axes of the tubes A and B, with the faces of which they make, consequently, an angle of 35 25'. The reflected portions of the pencils are then polarized in the plane of incidence, and the transmitted portions in the perpendicular plane. The reflected portion of the pencil A and the transmitted portion of B fall on the telescope L held by a tube F, diametrically oppo- Fio. 80. "Wild's Photometer. site to B. This telescope includes, beside the objective and the eye-piece, a double plate of quartz S and a Nicol prism JV, which together constitute a Savart polariscope ; it may easily be removed from the tube F and placed in the tube E, diametrically opposite A, in which fall the transmitted portion of the pencil A and the reflected portion of the pencil B. To use the apparatus we commence by putting the principal section of one of the plates of the polariscope in the plane of incidence of the rays which fall on the pile of plates of glass. This is accomplished by closing the opening A and turning the telescope until the fringes disappear. At this instant the principal section of one of the plates coincides with the plane of polarization of the portion of the pencil B which is refracted through the pile PHOTOMETERS. 71 of glass plates; consequently the principal section of the other plate is in the plane of incidence. We then turn the circle C of the tube B until the zero of the graduation comes to the zero of the vernier ; then after having undamped the screw V, we turn the polarizer P until complete extinction takes place in the telescope ; in this position the plane of polarization of the pencil which traverses P is in the plane of incidence. The polarizer of the tube A is regulated in the same way by placing the telescope at F. By a glance at the graduated circles we may know the angles which are formed with the plane of incidence by the planes of polarization of the pencils of light which emerge from the polarizers. This done, we proceed to compare the intensities of the lights L^ and L 2 . We may remark that for any position of the polarizers, the pencil of light transmitted by the pile and coming from B, does not have the same intensity as the reflected pencil coming from A. These two pencils polarized at right angles act on the polariscope like partially polarized natural light, and as they are slightly diver- gent, fringes appear. They disappear when the two pencils have the same intensity. If, then, x and a 2 are the angles which the planes of polarization of the polarizers A and B make with the planes of incidence, and <^ and d 2 the distances from the sources of in- tensity /! and 7 2 to the diifusers D, the intensity of the reflected pencil is ^Acos-a^ and that of the transmitted pencil -^B sin 2 o, Ctj Cl 2 A and B being the coefficients of diminution of the light passing through the diffusers and the polarizers ; accordingly, we have /, cL 2 B sin 2 whence 7 = 3 J d an equation which gives the ratio of the intensities when that of the coefficients A and B is known. This last ratio, which, theoretically, should be equal to unity when the different parts of the tubes A and B are identical, is determined experimentally, once for all, by inter- changing the position of the lights with respect to the tubes, and seeking new values of tq and 2 which make the fringes disappear. Assuming that the intensities of the pencils of light falling on the telescope are equal, we obtain a relation which, united with the pre- 72 PHOTOMETRY. ceding, permits the elimination of the ratio of the intensities and A the calculation of -B The method of Wild's photometer, then, depends on the phenom- enon of the disappearance of the fringes when two pencils of light of equal intensity and polarized at right angles are superimposed. This method allows, according to Wild, the comparison of the inten- sities of two lights within from -^-$ to y^Vff- ^s sensibility is then considerably greater than that of the Buiisen screen. It has, on the other hand, the inconvenience of fatiguing the retina, because of the persistence of the luminous impressions, and requiring a great deal of attention, for the eye frequently sees the fringes after they have dis- appeared, and it is only after a moment of repose that we can really be sure of their disappearance. For this reason, the exactness of this method is in reality less than the preceding figures would imply. Wybauw's Compensation Method. 46. This method* differs from the preceding methods; it con- sists essentially in this: one of the two faces of the photometer whose illuminations are to be compared receives in the ordinary way the rays from the light to be studied, an electric light for instance. The other face receives only a known or easily calculated fraction of this same light, a fraction to which is added as much of the light emitted by the photometric standard as is necessary to make the illuminations of the two faces of the photometer become equal. Wybauw has made a practical application of his idea in the con- struction of a photometer of the Foucault genus. In this apparatus, due to an ingenious arrangement of the mirrors, the path pursued by the rays of light projected 011 one of the surfaces to be illuminated is increased in a suitable ratio, relatively to the path of the rays of light projected on the other surface ; a carcel lamp then serves to equalize the difference thus obtained in the illuminations of the two surfaces. The Compensation Photometer of Kruss. Krtiss has realized Wybauw's idea in quite a practical manner by employing the Bunsen photometer f. Let /! and / 2 be the lights to be compared, E the photometric screen, BD a mirror whose plane makes an angle c with the line IJ* * Bull, de la Soc. beige des electriciens, Vol. II. No. 5. t Lum. til., Vol. XIX. p. 118. PHOTOMETERS. 73 The photometric screen E receives, then, on one side the light which comes directly from J 1? on the other side the light from the same source which has just met the mirror BD and been reflected along the path I^AE, and finally the direct rays from the light 7 2 . It is easy to determine the exact formula for the apparatus. The formula which Krtiss gave at first has been advantageously modified by Strecker*. We will confine ourselves to giving the results of the latter without entering into the details of their calculation ; for, since the invention of G-rosse's mixture photometer, which solves the problem of compensation in a most perfect manner, Kruss's compensation photometer has lost its importance. FIG. 81. Compensation Photometer^ Below are Strecker's conclusions. Designating by a the hori- zontal distance from the axis of rotation of the mirror BD to the screen E, the angle e must be comprised between 60 and 70, and the distance from the unknown light J x to the screen must be comprised between 10 a and 15 a. Under these conditions, the formula to be employed is in which + o- cos 2 The coefficient of absorption of the mirror (about one per cent) is represented by o-, and represents a constant whose values are, for * Elel-tr. Zeitschrift, 1887. 74 PHOTOMETRY. = 60 = 8.8 65 17 70 25 The coefficient k should not exceed 3. 75 31 Grosse's Mixture Photometer. 47. This photometer * depends at the same time on the employ- ment of Wybauw's compensation method and on phenomena of polarization. It includes a prism Pof spar (Fig. 32), formed of two rectangular isosceles prisms abd, bed, separated by a thin layer of air, and cut with reference to the optical axis of the crystal so that the ordinary ray coming from an incident ray normal to one of the faces is totally reflected at the diagonal plane bd. Consequently the incident pencil V will give, in the direction UR, a pencil polarized K FIG. 82. FIG. 33. perpendicularly to the plane of incidence, and the incident pencil T will give in this same direction a pencil polarized in the plane of incidence. In Grosse's photometer the pencils which emerge from the prism P fall on a nicol N (Fig. 33), whose principal section makes with the plane of the figure an angle measured by the movement along the divided circle KK oi an index on the tube M. Totally reflecting prisms A, B, C, D reflect in suitable directions- the rays which traverse the plates of ground glass G and H cut from the same sheet and illuminated by the lights to be compared. * Zeitschrift fur Instrumentenkunde, 1888, pp. 95, 129, 347 ; Lum l.> Vol. XXXI. p. 221 ; and Butt des sc, phys. , Vol. I. p. 583. PHOTOMETERS. 75 Finally, screens E and F } moving in two slots, permit us to limit the pencils of light which enter the instrument. If the screens are in the position indicated in the figure, the left half R of the field of the instrument is illuminated by the pen- cils S and Si', the first coming from the light S, and the second from the light S lf The other half T of the field is illuminated by the pencils 2' % and Si- These pencils have the same section, and consequently cut on the plates of ground glass G and H equal sur- faces g, g', b, &', whose area may be taken as unity. The pencils S' and Si', undergoing the same transformations, have the same coeffi- cient of diminution A ; for a like reason, the pencils S and Si have the same coefficient of diminution B. If, now, we designate by 7 and Ji the intensities of the sources, by d and di their distances to the plates G and H, and by a the angle of the principal section of the analyzer N with the plane of the figure, we have for the inten- sities of the rays emerging from the analyzer and coming from the pencil S B cos 2 , Cv S' A- 2 siu z a, Cv Si -Bcos'o, i sn a. df The screen F being so inserted as to intercept the pencil Si', when the two portions of the field of the instrument are equally illumi- nated, we have 2 B- cos 2 = A, sin 2 a + B\ cos 2 a. d 2 d 2 d^ If the screen E is inserted so as to intercept the pencil 2', the screen F being withdrawn, we have, when the field is uniformly illuminated, &L cosV + A sinV = B i cosV, d 2 df df a' corresponding to the new position of the analyzer. Eliminating A and B in the two preceding equations, we have an equation which gives the ratio of the intensities. 76 PHOTOMETRY. According to the preceding, the comparison of the intensities of A the two sources necessitates two operations ; but the ratio ~(=k) is a constant of the instrument ; it may be determined once for all. When it is known, the ratio of the intensities is deduced by a single operation from the formula J d 2 1 Kruss of Hamburg, the maker, has given the apparatus, a prac- tical form which allows it to be fitted directly to the photometric bench in place of the Bunsen arrangement (Fig. 34). The split rectangular prism P, the triangular prism A, both of calcarious spar, and the three totally reflecting prisms B, C, D are placed in a closed box C ; the lateral walls of this box are made of FIG. 34. Grosse's Photometer. two plates of ground glass G and H 2 (at ?% and ra 2 ). On the back of the box C are found two buttons Si and S 2 which govern the screens E and F. The front has a circular opening through which the rays of light pass, to fall afterwards on the Nicol prism N placed in the tube R. The Nicol prism is movable about the axis of the tube, and an index indicates the rotations on the divided circle K. When the index of the Nicol prism is on the zero of the scale, either the ordinary or extraordinary rays must be extinguished; the regulating screw allows this result to be exactly obtained. This photometer may be employed in different ways, either as an ordinary photometer without compensation, by pushing the two screens E, F entirely in, or as a unilateral compensation photome- PHOTOMETERS. 77 ter, by withdrawing only one of the screens, or finally as a bilateral compensation photometer, by withdrawing both screens *. Grosse has perfected his apparatus | by adding, between the spar prism and the analyzer N, a Soleil double-rotation plate of quartz, which introduces phenomena of coloring by polarization. The meas- urement consists then in obtaining equality of the tints of the two regions by moving the lights to be compared. We cannot enter into the details of this modification. D. PHOTOMETERS BASED ON VISUAL ACUTENESS. (HETEROCHROMATIC PHOTOMETRY.) General Methods of Heterochromatic Photometry. 48. In all that precedes, we have supposed implicitly that the two lights compared have the same tint ; that is, that the rays emitted by the two lights have the same composition. However, this is not the case in reality. The light chosen as a photometric standard generally emits rays whose composition differs from that of the rays emitted by the light which is studied. As a result the two divisions of the photometer whose illuminations are to be equalized are differently colored, which renders the measurements very uncertain, if not impossible. It is in fact difficult to judge exactly of the equality of illumination of two surfaces of different tints; this is only accomplished in practice in an approximate and wholly conventional manner, for the impressions are of dif- ferent natures, and the same observer, with an interval of only a few minutes, does not come to the same conclusions ; a fortiori two observers may obtain different, or even contradictory results. It should be added furthermore that the optical illusion, on account of which the line of separation of the two illuminated divisions of certain photometers disappears at the instant of equality, no longer exists, which deprives these photometers (Foucault, Joly, Elster, Lummer, etc.) of a considerable part of their exactness. For this reason von Helmholtz has been able to say that " of all the comparisons effected by the aid of the eye between the intensi- ties of different sorts of composite light, there is not one which possesses an objective value independent of the nature of the eye." Fortunately this assertion is not rigorously true, for measure- * Lum. til., 1889, Vol. XXXI. p. 224. t Chemiker Zcitung, 1887, No. 94. 78 PHOTOMETRY. meats of relative intensity would then be about impossible in the great majority of cases, since it is rarely that we find two lights of exactly the same tint. The obstacles to an exact comparison of two lights of different tints are the result of a singular property of the eye discovered by Purkinje*, which von Helmholtzf has thus enunciated: "Intensity of sensation is a function of the luminous intensity which differs with the kind of light." Intensity of sensation increases and decreases more slowly for the blue than for the red, for the same variation of objective luminous intensity. To be definite, let us consider two sources of colored light, one yellow and the other blue, and let us put them before a Rumford photometer (3 18) so that the two shadows of the opaque pencil, placed in front of the white screen, appear equally bright. If we simultaneously double the quantity of light thrown upon the screen by the two sources, we shall find that the yellow shadow appears brighter than the blue shadow, while if we reduce to one-half of their original values the quantities of light thrown by the two sources, the blue shadow will appear brighter than the yellow. Consequently if we wish to express the intensity of the blue light as a function of the intensity of the yellow taken as unity, we shall find a number which varies according to the conditions of the comparison. The number which should represent the intensity of the blue light will be found less when we employ a greater quantity of yel- low light to effect the measurement, and, on the contrary, greater when the chosen quantity of yellow light is less. It follows from what precedes that if a reddish light, as that of the carcel lamp, is compared with a bluish light, as that of the arc lamp, the ratio of the intensities varies with the illumination of the photometric field. In the single case when the intensities of brightness of the two halves approach zero, does the photometer give ratios which are independent of the absolute value of the intensities. This, as Crova has shown, explains why Allard has been able to determine with sufficient precision the ratio of the luminous intensi- ties of radiants of very different tints, by taking the precaution to half close the eye while looking at the photometric screen ; by * Zur Physiologic der Sinne, Vol. II. p. 109. t Optiqne Physiologique, \\ 4'21 (French translation). PHOTOMETERS. 79 so doing the approach of the eyelids cuts off, like a diaphragm, the pupillary opening more and more, and the intensity of the retinal field tends toward zero, the limit near which all sensation of color disappears, the luminous impression being still sufficient to enable one to judge of the equality of the two regions, which then appear a uniform gray. The preceding facts show that the comparison of luminous intensities of differently colored radiants should depend on other methods than those which are in use in the photometric comparisons of lights of the same color. Before explaining these methods, let us recall that, in general, two quantities of light are equal to one another, when, received by the eye of the same observer, they pro- duce on him the same effect ; but this effect should be independent of the coloring of the light, and only dependent on its intensity. These two conditions may be satisfied in two ways, as Mace de Lepinay and Nicati* have shown, taking as a starting-} loint two quite different functions of the eye which correspond with sufficient exactness to the two expressions to distinguish and tb see. 49. The first method is based on the following phenomenon: If light of any color and of an. intensity which grows less and less, falls on a printed page, we experience an increased difficulty in reading, and the observer, to distinguish the characters, must approach nearer and nearer the object. It is this which is expressed when we say that cisual acuteness diminishes with diminution of in- tensity of illumination. Let us recall that visual acuteness is measured by the reciprocal of the angle under which a definite object (ordi- narily printed characters) must be seen in order to recognize its form. This fact is intimately connected with intensity of illumination, or, more exactly, intensity of ths light perceived by the eye, and more- over is completely independent of the nature of the color impressions produced on the eye by the light which produces the illumination. We may then form a basis for a photometric method by con- sidering two quantities of light equal when, fatting on the same uncolored object (black on a white background) always placed at the same distance from the observer, they enable him to perceive, the details with the same nicety, or in other words, when they reduce the visual acuteness to the same value. This method was invented by Celsius and employed afterwards by W. Herschell. * Ann. de Chim. et de Phys., 5 e s6rie, Vol. XXIV. p. 289 ; Vol. XXX. p. 145. 80 PHOTOMETRY. We know that visual acuteness is measured by presenting to the eye letters of different sizes, placed at an invariable distance (five meters, for example), and noting the dimensions of the smallest letter which is clearly seen. Another method which is more exact consists in employing signs of definite sizes and having the observer approach until he begins to distinguish them. The visual acuteness is, in this case, directly proportional to the distance from the observer to the object at the moment when he perceives it distinctly. The letters which are used are made of heavy black lines whose width is equal to the interval between them. We take as the unit of visual acuteness (v = l), an acuteness such that for the observer the distance between the consecutive lines subtends an angle of 1'. If the width of the lines is 1 mm., the visual acuteness is 1 when the distance from the observer is 3.44 in. At a distance of 1 m., the visual acuteness is v-^ = - =0.29, and at n m. it is Vn = 0.29n. Mace de Lepinay and Nicati have found that it is preferable, for photometric measurements, to replace the letters by three black horizontal lines on a white background, 5 mm. long, 1 mm. wide and 1 mm. apart. To obtain lines perfectly black, the most simple method is to cut them in a sheet of white waxed paper, and to place the sheet before a cavity lined with black velvet. In this way the black lines reflect only a negligible part of the light which strikes them. In order to compare the intensities of two radiants by this- method, we may proceed as follows : We illuminate the conventional signs adopted to determine the visual acuteness by the light from the photometric standard, placed at a definite distance d x ; then the observer approaches until the eye, at the distance d, clearly perceives them. Next we illuminate- them by the radiant to be studied, which is moved until the observer perceives them anew with the same facility as before. Let f7 2 be the distance of the radiant corresponding to the limit of perception. At this instant the visual acuteness is the same as before, and consequently the illuminations are equal, /j being the intensity of the photometric standard, / 2 that of the radiant which is studied,, we have, whence PHOTOMETERS. 81 In practice we may employ with advantage as conventional signs the logarithms of any table; the detached page of the table plays the part of the screen on which the numbers appear with more or less clearness, according to the intensity of illumination. This method should only be employed when the two radiants to be compared are very differently colored, for its precision does not exceed about 10 per cent ; this degree of precision may be considered satisfactory for differently colored radiants, but it would not be sufficient for lights of the same tint. !jjji 50. Beside the preceding method based on visual acuteness, that in which equality of illumination of two continuous divisions is determined directly may also be used for the comparison of radiants of different tints, but with an important restriction. When two neighboring divisions are illuminated, the one exclusively by one of the radiants, the other exclusively by the other, experience shows that however different the coloring of these two contiguous, divisions may be, provided they are small enough, the eye may appreciate with a certain exactness the moment when these two divisions appear equally illuminated. The restriction mentioned above is relative to the dimensions of the divisions whose equality of brightness is to be established. The eye appreciates in fact with correspondingly greater difficulty the coloring of a surface, as this surface becomes smaller. It follows from the very complete measurements of Mace de Le'pinay and Mcati that the two regions illuminated by the radiants com- pared should subtend an angle less than 45'. Consequently the size of the divisions should not be greater than 6.5 mm. if the observer is at a distance of 50 cm. Below are the limit values of the size of the divisions for various distances of the observer. Distance. Size. 0.1 m. 1.3 mm. 0.3 3.9 0.5 6.5 1.0 14.1 2.0 26.2 3.0 39.2 5.0 65.5 The limit value which the size of the illuminated division should not exceed for a given distance of the observer, is so deter- 82 PHOTOMETRY. mined that the ratio of the intensities of the two radiants of different tints may be independent of their absolute intensity or, at least, not depend on it more than on Purkinje's phenomenon. For this the retinal images should be smaller than 0.002 mm. which corresponds to a visual angle of 45' : this value is exactly 0.002 mm. for the blue, and 0.004 mm. for the red. In the majority of lights, the most refrangible radiations are the least intense ; we may almost always double the values of the limit sizes, which results in giving to the visual angle a value of 1 30'. This method consists, then, in employing, for the comparison of differently colored radiants, the usual photometers, taking care that the size of the divisions whose illuminations are to be made equal do not exceed the above limits. The preceding is sufficient to give an idea of the two principal methods which may be used in the comparison of lights of different colors. It remains for us to enter into the details of the methods and the practical apparatus. Mace de Lepinay's Method*. 51. This method depends on the following fact demonstrated by experiment, which has enabled Crova to establish his method for the optical measurement of high temperatures. When bodies of the same temperature and of different emissive powers are placed in obscure surroundings, they emit light of very different intensity, but of the same composition. This law is directly applicable to the usual radiants which are all constituted of particles of carbon rendered incandescent by the high temperature to which they are brought. Let / be the intensity of a radiant, deduced by direct comparison with the photometric standard, e.g. the carcel lamp. Let us desig- nate by R the intensity of one of its red rays, of determined wave- length, measured by the spectro-photometer with reference to the intensity of the same kind of ray of the carcel lamp; and by G the intensity of one of its green rays, denned in a similar way. If for the first radiant another at the same temperature is substituted, the three quantities J, G, and R remain proportional, and the two ratios and retain the same values. H R * ComrtP* Timdus, Vol. XCVII. p. 1428. PHOTOMETERS. 83 If the temperature of the radiant studied varies in a continuous manner, it will be the same with the composition of the light which it emits, and the two ratios and will vary also in a continuous R R manner. We shall then be correct in writing The intensity of any ordinary radiant could then be determined by simply measuring the intensities G and R. if the nature of the fC*\ function/( ) were known in advance. \RJ This solution of the problem would not be practical, for it would necessitate the employment, always delicate, of a spectro-photometer. But the exactness of the entire reasoning remains if we substitute for the spectro-photometric measurements made with rays of deter- mined wave-length, in the red and the green, measurements made by means of the Foucault photometer. The divisions should then be observed through two solutions, one red, and the other green; these solutions should always be employed in the same state of con- centration and of the same thickness ; they should in addition fur- nish rays sensibly simple, in order that the two divisions of the screen may have the same color. The solutions which best fulfil the above conditions are : a solu- tion of pure perchloride of iron in water at 38 B. (Baume), and a solution of pure chloride of nickel in water at 18 B. The two solutions should have a thickness of 3 mm. The first transmits red rays only, and the second green rays only. To determine by experiment the function /( ], Mace de Lepinay W made 52 measurements, comparing with the carcel standard succes- sively, a regulating lamp with a straight chimney, one with a bulging chimney, a petroleum lamp, the Drummond light, and finally sun- light diffused by a white screen of sulphate of barium. The following formula is deduced from these measurements : .Zi/ -i * r\ f\i By means of this formula the following numerical table, which is sufficient in practice, was calculated : 84 PHOTOMETRY. R 7 R R / R 0.8 0.96 2.0 .26 1.0 1.00 2.2 .33 1.2 1.04 2.4 .41 1.4 1.09 2.6 1.50 1.6 1.14 2.8 1.60 1.8 1.20 .... The degree of exactness which this method gives is shown by the following verifications : With a Swan lamp (at 12 volts and 0.95 amp.) Mace de Lepinay found : G = 0.167, whence 0.184; = 0.908, then I = 0.180. Direct experiment gave / = 0.182. With the Drummond light, the following results were obtained : G = 6.59, R = 5.04 ; whence = 1.31, R . l =1 - 07; that is, / = 5.39. Direct measurement gave / = 5.43. PHOTOMETERS. 85 L. Weber's Photometer. 52. The preceding formula of Mace de Lepinay may be put in the form representing by / the intensity of the radiant obtained by the method of equal illumination, by R the intensity of the red light obtained by means of a solution of perchloride of iron in water at 38 B., and by fc a coefficient which takes account of the physio- logical elements of the problem, and which is, according to the measurements of Mace de Lepinay, 1 V In this equation G represents the intensity of the green light obtained by passing the rays of light through a solution of pure chloride of nickel at 18 B. Weber's photometer permits the easy measurement of the inten- sities G and R, by the aid of which the intensity / is deduced from the preceding formula*. It is composed of a horizontal tube A (Fig. 35), in which are placed the photometric standard H, and a ground glass s, whose movements, parallel to the axis of A, are governed by the screw /, and may be measured with very great exactness. At one of the extremities of A, and movable about the axis of this tube, is found a second tube B, provided in the same way with a ground glass s^ it has at g an opening before which the eye of the observer is placed. When the tube B is directed at any radiant, the vertical edge on the left of the prism of total reflection P (Fig. 36) divides the visual field into two portions ; the half at the left is found to be illuminated by the observed radiant, and the half on the right by the standard of comparison H. Moving the glass s from right to left, and, if necessary, making use of the glass s x , we succeed in obtaining perfect equality in the illumination of the two halves of the visual field. Under these circumstances it is sufficient to place before the eye a plate of glass which has been made red by means of a deposit of suboxide of copper, in order that the two visual fields may appear * mektrotechnische Zeitschrift, Vol. V. p. Ififi ; Lnm. EL, Vol. XII. p. 468. 86 PHOTOMETRY. absolutely monochromatic, even when the tints of the radiants compared differ notably from one another. Weber was not satisfied with the values of the coefficient k deduced from the formula of Mace de Lepinay ; he determined this coefficient directly by means of his apparatus and two plates of ground glass on which particular designs were photographed. These two plates are fitted to each piece of apparatus, which enables one FIG. 35. Weber Photometer. to verify, by the method of equal visual acuteness, the results obtained by the method of equal illumination. These plates are obtained in the following way : first there are drawn, on a rectangle of paper 40 cm. by 20 cm., eight squares in which are traced concentric circles in which the width of the white of each circle is equal to the width of the black. A photographic reduction to a twentieth gives very clear plates, 2 cm. by 1 cm., in which the width of the eight systems of circles varies from 0.275 mm. to 0.1 mm. by steps of 0.025 mm. PHOTOMETERS. 87 These plates are placed one at s and the other at s l ; they occupy only one-third of the corresponding half of the visual field. The plate s l being fixed, the plate s should be at the division 245 mm., in order that the designs of the two plates may be seen by the observer, subtending the same angle. If the two parts of the visual field are equally illuminated by radiants of the same color, the clearness of the designs is the same in both parts ; but if the tube B is directed at a radiant whose tint differs from that of the other, and then the equality of the light of FIG. 36. the two surfaces is established, the designs will not be equally clear in the two halves of the visual field. The phenomenon is due to the fact, enunciated by Mace de Lepinay, that in the spec- trum, as we go from the green, the refrangible colors contribute little to clearness of perception while contributing in a considerable measure to illumination of the surfaces. Two observations should be made. The plates being put in place, B is directed at any radiant ; then the photometer is moved backwards or forwards until the designs appear on the two plates with equal clearness. This point is determined in a way which is precise and inde- pendent of the sight of the observer, by at the same time fixing the 88 PHOTOMETRY. two designs, and turning one's gaze from the largest to the smallest circles. It then happens that for a square of a certain order, the white cannot be distinguished from the black ; the right point is reached when the square in each of the two plates, for which this distinction becomes impossible, has the same number. At this moment the red glass is placed before the eye, and without further considering the designs, the equal illumination of the surfaces which are outside the photographic plates is brought about by moving the glass s. Let us suppose that s has been moved r cm. from 0; the value of k will evidently be (1M.5) 2 This value of k is not absolutely independent of the intensity of illumination which has served to establish the equal clearness of the designs; therefore the flame of the standard should be maintained- at as invariable a height as possible. For radiants which include more yellow and less red light relatively to the ascetate of amyl lamp employed as a standard, r is found greater than 245 mm. The value of k becomes equal to 1 when the light considered has the same color as the flame of the standard. Weber undertook a second series of experiments to determine the variations of k with the color of the radiant. The surfaces are illuminated equally for the red light, s remaining fixed at 245 mm., then a green glass is substituted for the red glass, and the new movement p of s is noted by which the equal illumination of the surfaces is established anew. These measurements are repeated for different tints 'of the radiant which are obtained by raising a lamp to more or less incandescence. Under these circumstances the ratio of the intensities G and R of the green and the red, compared with the same colors of the ascetate of amyl lamp, is expressed by Spectroscopic researches have shown that the red glass used in connection with Weber's photometer, lets pass only those rays included between the wave-lengths 0.687 /x and 0.630 p, whose maxi- mum intensity corresponds to 0.656 /x, and the green glass only those between 0.577 /x and 0.516/x, with a maximum at 0.547 /x. PHOTOMETERS. 89 At the same time as Weber, Dr. 0. Schumann determined by the aid of Glan's spectrophotometer ( 66) the value of the ratio of the green and red radiations from an incandescent lamp, compared in the same way with radiations of the same color from an ascetate of amyl lamp; the wave-lengths of the -radiations compared were A = 0.6762 /x and \ = 0.5574 /x. These values differing slightly from one another, Weber con- structed curves which gave the mean value of k included in the following table: G R k G R k 0.3 0.50 1.3 1.22 0.4 0.56 1.4 1.28 0.5 0.64 1.5 .34 0.6 0.72 1.6 .40 0.7 0.80 1.7 .46 0.8 0.87 1.8 .51 0.9 0.94 1.9 .56 1.0 1.00 2.0 1.61 1.1 1.08 2.1 1.65 1.2 1.15 2.2 1.69 This table is sent out with each piece of apparatus. Practical measurements then offer no difficulty. We obtain the points d r and d g , corresponding to the equality of illumination of the two divisions of the photometer for red and green radiations, by inserting successively in the movable tube plates G_d r 2 We then have = -^, and, seeking in the R d~ of red and green glass. above table the corresponding values of k, we obtain a being a factor which depends on the coefficient of absorption of the ground plates of the photometer and on the intensity of the standard flame. It is easy to determine this constant a once for all. We may remark that the values of Jc obtained from the preceding table give results which are only precise for the photometric com- parisons of radiants whose light has an analogous composition to that which is emitted by incandescent lamps under ordinary circum- stances. 90 PHOTOMETRY. If the radiants compared emit light of the same tint, k = 1. We may then make the comparison without employing colored glasses ; if it is desired to use them, it is sufficient to make an observation with one of them merely, the ratio of the intensities of the red and green radiations being equal to the ratio of the total intensities. 53. L. Weber has recently * perfected his apparatus by the introduction of Lummer and Brodhun's optical screen (31) and by the substitution of polarization apparatus for the screens designed to equalize the illumination of the two halves of the visual field. This new model really belongs to the class of polarization pho- tometers. Figure 36 shows the arrangement of this new piece of apparatus. The prism-screen of Lummer is put in place of the total reflection prism of the older model. In the movable tube B are found two nicols a and b, whose relative position determines the intensity of illumination of the outer part of the photometric field ; the illumi- nation of the inner part of the field is regulated in the ordinary manner by the movement of the opalescent screen s. Two methods may be employed in making the comparisons. In the first, the nicols are placed in their parallel position (a = 0, (3 = 90, or, a = 90, (3 = 0), so that there is no weakening of the light which traverses them, except what is produced by absorp- tion. Next the illuminations of the two halves of the field are equalized by moving the opalescent screen s. The second method is preferable. The plate s is left in a fixed position, then the nicol b is turned until the two halves of the visual field are equally illuminated. The weakening effected is easily calculated by means of the equation of Malus, the intensity of the exterior field being given by the formula -^sin 2 ( ft). In this formula c represents the constant of the nicol, d the fixed distance of the opalescent plate. We may also determine empirically the weakening corresponding to a determined position of the nicol b and make in advance a table for each piece of apparatus. This second method renders the division of the fixed tube A useless. The exterior tube R serves to keep lateral light from the bare plate while measurements of illumination are being made. The two nicols a and 6 are placed between the plate s' and the prism P; for if one of them, 6 for example, were placed between the * Zeitschrift fur Instrumentenkunde, 1891, p. 7. PHO TOMETEE S. 91 prism-screen and the ocular prism, complications in the formulae would result. A part of the light reflected by the exterior part of the screen and coming from A is polarized by reflection ; account should then be taken of this fact in the formulae. The tube B is fitted with an ocular prism of total reflection in order to facilitate observations when it is in a vertical position. Crova's Method. 54. Whereas the method invented by Mace de Lepinay reduces the photometric comparison of two lights of different tints to the comparison of the intensities of two of the component colors, Crova* has invented a method which requires only the comparison of the intensities of a single one. This method depends on a fact verified by a great number of experiments. It may be enunciated as follows : if two lights of very different tints are compared, the total intensities are to one ait other as the intensities measured in that part of the spectrum where the wave-length is 0.582 /x. The following is the manner in which Crova arrived at this con- clusion. He measured by means of the spectrophotometer the luminous intensity of different regions of the spectrum of sunlight and of the light of the carcel lamp, taking in each series as unity the hundredth part of the intensity of the most intense radiation. Tracing the two curves whose abscissae are the wave-lengths and whose ordinates are the illuminating powers, the area of each of them represents for each light the total illuminating power. Crova deter- mined with care the ratio of the areas of the two curves furnished by sunlight and the carcel lamp, and obtained the fraction 0.7302. If the ordinates of the curve of intensities of sunlight are divided by 0.7302 while retaining the curve of the carcel lamp, the two areas are then equal, and the curves correspond to equal illuminations. These two curves cut one another at a point whose abscissa corresponds to X = 0.582 /A; this radiation is then that whose intensity is the same in the two lights when the two illuminating powers are equal. The preceding comparisons having been made with the light of a radiant of low temperature, as the carcel lamp, whose maximum illumination is at the radiation X = 0.592 /*,, and with sunlight which has the highest temperature of emission, and whose maximum is at X = 0.564 /x, the preceding conclusions may be applied directly to * Comptes Rendus, Vol. XCIII. p. 512; Ann. de Chim. et de Phys.,6* s6rie, Vol. VI. p. 528 ; Lum. l., Vol. XVIII. p. 549. 92 PHOTOMETRY. the usual radiants, whose temperatures of emission are comprised between these limits. This method cannot be applied to the photometric study of a radiant whose temperature of emission varies with the luminous intensity; incandescent lamps are in this class. The luminous in- tensity increases with the energy spent in the lamp, but the pro- portion of the radiations of different wave-lengths varies also. Weber's method, in which the luminous intensity for a single wave-length is measured, is free from this restriction, because the coefficient k is determined experimentally for different degrees of incandescence. To obtain an exact comparison by Crova's method, it is necessary to use a spectrophotometer, and to bring the middle of the ocular slit to a point on the graduation which corresponds to A = 0.582 //,. ]>ut, in practice, we may work in a more simple and rapid manner by the aid of one of the two following methods. In the first, we employ the ordinary Foucault screen, or any screen that is viewed by means of a telescope whose objective, of short focal length, allows a very clear image of the disc and of the line of separation of the two regions to be obtained. In the body of the telescope there is a system of two nicols, placed at right angles, between which there is a pl.ite of quartz ( .) mm. thick, perpendicular to the axis; this thickness has been calculated so that its interposition between the two crossed nicols gives rise, in the spectrum of the light which traverses them, to two wide interference bands situated at the two extremities of the spectrum, which in this way almost extinguish the intensity in these regions. In going from these two bands toward the limit of the yellow and the green, where the wave-length is 0.582 /A, the intensity of the transmitted radiations varies in proportion to the square of the cosine of the angle made by the right section of the second nicol with the planes of polarization of the different radiations which have undergone in the quartz plate rotary disper- sion ; the radiation for which the cosine is equal to unity undergoes no diminution. The apparatus is regulated so that the radiations in the im- mediate neighborhood of 0.582 ^ undergo no diminution. In the second method, which is much simpler, the photometric screen is observed through a special solution which allows only radiations whose wave-length is about 0.582 /x to pass. This solution, which produces considerable absorption, is more specially applicable to very in "ens > radiants. PHOTOMETERS. 93 The solution is prepared thus : Anhydrous sublimed perchloride of iron . . 22.321 grams. Crystallized chloride of nickel 27.191 " It should be dissolved in distilled water, and the volume of the solution made 100 cc. at a temperature of 15 C. The liquid is contained in a glass receptacle with parallel faces, the surfaces in contact being ground. The receptacles which Crova used consist of a flat ring of glass 7 mm. thick, ground smooth, against the faces of which are fixed, by simple adhesion, using a drop of distilled water, two thin sheets of plate glass with accurately parallel faces, pressed against the ring by means of two blackened brass plates with four pressure screws ; the two pl-ites have circular openings whose diameter is slightly less than that of the receptacle, so as to allow only the rays which traverse the liquid to pass through. The liquid is introduced by means of a capillary pipette through a small orifice in the ring which is afterwards closed by a ground glass stopper. To avoid the possible breaking of the glass on account of too strong pressure of the screws, it is well to insert between the receptacle and the glass plates, washers of cardboard or leather. Receptacles thus filled last a long time without alteration. With a thickness of 7 mm. this solution allows to pass only radiations comprised between the wave-lengths 0.630 /a and 0.534 /x, with a maximum near 0.580 //, ; if the thickness is increased, these limits approach one another and tend toward a maximum of from 0.580 ju to 0.582 p., which is the most favorable. Temperature has a notable effect on the absorbing power of perchloride of iron ; in proportion as it increases, the absorption increases in the most refrangible region, and the black screen which appears to cover the spectrum up to the limit of the green advances toward the red. The limits of the wave-length indicated above are then variable with the temperature, but at about 13 C. these limits are sensibly invariable for small variations of temperature. The Employment of Media of Complementary Color. 55. The study of heterochromatic photometry would be incom- plete if we passed in silence the employment of glass of comple- mentary colors, designed to eliminate errors due to differences of color in the lights compared. 94 PHOTOMETRY. Tresca first proposed to insert between the radiants and the screen plates of glass of about complementary colors. He invented this process on the occasion of the photometric measurements of arc lights at the Electrical Exposition of 1881. A green glass is placed in the path of the reddish rays of the standard, the carcel lamp, and a red glass in the path of the bluish rays of the arc lamp. If the colored glasses that are thus inter- posed were exactly complementary to the rays from the correspond- ing radiant, all the rays would be intercepted, and the two fields of the photometer would remain dark ; but as glass of about complemen- tary color is employed, we shall find on either side a dull gray color whose tone will be sensibly the same on both sides. But if the color of the two fields of the photometer is made equal, it is diffi- cult to see how account may be taken of the quantity of light absorbed, on both sides, by the two colored glasses. Tresca seems to assume a priori that these losses are equivalent, i.e. that the red rays lose as much in the green plate as the green rays in the red plate, which is anything but proved. If we wish to measure experi- mentally the value of these losses, we would be brought anew to the comparison of the relative intensities of two very differently colored lights, and that is exactly what we wish to avoid. Tresca's process lacks, then, a precise scientific basis. A second method based on the employment of glasses of com- plementary color has been sometimes proposed. It consists in mak- ing two measurements by observing the screen successively through two glasses or two special media, which allow only exactly comple- mentary rays of light to pass. The arithmetical mean of the results of these two measurements is then considered the exact result. This method cannot give exact results, for it is only a rude approximation to the scientific methods of Mace de Lepinay and Weber. We may, however, establish with sufficient ease the con- ditions which the two colored media and the lights we are compar- ing should satisfy in order that the process may be strictly exact. Let us consider two exactly complementary glasses, e.g. red and green. Let us designate by 7 : the intensity of the first radiant, by GI and RI this intensity measured through green and red glass respectively. Let us further designate by J 2 > #2? and R 2 the same elements of the second radiant. We have evidently the following relations : PHOTOMETERS. 95 Let us designate by k the ratio of the total intensities : T If the two radiants L and L z should emit light of the same quality, that is, have similar spectra, we should have J 2 = M, = kGj. But this is not the case, the relation being The two coefficients a and b vary with the quality of the light from LI and L 2 . If one of these is smaller than Jc, the other must be greater. Let a = k x ; then whence & = i - - * In order that the arithmetical mean of the measurements may be exact, a -f b should be equal to 27c, that is, b = 7c + x. But we have and, substituting for kI L its value, In order that this condition may be satisfied, it is necessary that #! = R lm These- two colored media should accordingly be not only complementary, but they should absorb the same quantity of light : the luminous pencil which has passed through the first medium should have the same value as after having traversed the second. The verification of this property of colored media is as difficult as the comparison of the two radiants, since it is necessary to verify the equality of the two lights, the one yellowish red, and the other blu- ish green. Moreover, the construction of these two exactly comple- mentary media would not be without difficulty. We have not space to dwell further on this process. [For another method see Appen- dix B.] 96 PHOTOMETRY. * R PHOTOMETERS BASED ON VARIOUS ACTIONS OF LIGHT. 56. No apparatus in which the action of light on the eye is replaced by its action exerted on physical or chemical phenomena, independent of the observer, is suitable for photometric measure- ments. Such apparatus measures the action of light upon the phe- nomenon on which the instrument is based, but it does not measure in any way its physiological action. Such are chemical photometers which have, however, their importance from a photographic point of view, selenium photometers, etc. Although this apparatus does not fulfil the principal condition of photometric measurements, nevertheless it should be mentioned, since it alone permits the effectual automatic registering of photo- metric measurements. This registering is in fact impossible with ordinary photometric apparatus, since the eye is its principal organ. Among the photometers of this category, we should mention principally Siemens's selenium photometer and the photometers of Dessendier and of Lion. We should mention, also, the bolometer of which Langley made such extended use in measuring the distribu- tion of energy in the spectrum, and the radiometer of Crooks, of which Olivier* has constructed a special form for photometry. Selenium Photometer. 57. It is known that the electrical resistance of selenium dimin- ishes under the influence of light; it is the luminous rays which most affect it ; calorific rays exert a much less marked effect. Mak- ing use of this property, Siemens and Halskef about ten years ago invented their selenium photometer. A selenium tube replaces the screen of the ordinary photometers. This tube is placed in circuit with a battery and a mirror galva- nometer. First it is submitted to the rays of the photometric stan- dard, and the deflection of the galvanometer is noted, then it is turned so as to be exposed to the rays of the radiant to be studied. Next, the distance of the selenium plate to the radiant is varied until the deflection of the galvanometer is equal to that produced by the standard. In this case the illuminations produced by the stan- dard and the unknown light are equal. * Lum. El., Vol. XXVII. p: 560. t Lum. &., Vol. IV. p. 367 ; Vol. VII. p. 38. PHOTOMETERS. 97 Gime* also has invented a photometric method based on the employment of a narrow ribbon of selenium, rolled up so as to form a surface of considerable size which is placed in the circuit of a con- stant cell. Dessendier's Registering Photometer. 58. This photometer is based on the following principle : If a mixture of equal volumes of hydrogen and chlorine is kept in the dark, the two gases do not combine. If this mixture is exposed, there is combination, and as a consequence the formation of hydro- chloric acLl. This may be absorbed by a chlorine solution whose level tends to rise. Now, the quantity of hydrochloric- acid pro- duced being, according to Dessendier, proportional to the quantity of light received by the gaseous mixture, it is. sufficient to regis- ter the variations of the level of he chlorine solution in order to register the variations of the quantity of light received f. This photometer registers the chemical action of light on a mix- ture of hydrogen and chlorine, and not its photometric action ; so everything points to its employment in photography, where it has, moreover, been applied to the automatic printing of proofs. It is a long step from this to the application of this apparatus to industrial photometric measurements. If we limit ourselves strictly to regis- tering the luminous intensity of a given radiant, the selenium photometer permits the problem to be solved more simply, since it reduces it to recording the variations of intensity of a current. Lion's Photometric Balance. 59. Lion's photometer $ is based 011 the decomposition of iodide of nitrogen by the action of light. This substance decomposes slowly with a disengagement of pure nitrogen which varies with the intensity of the incident light. G-uiard determined that only the portions of the iodide which are directly struck by the luminous pen- cil undergo this decomposition, it being purely superficial. Lion has arranged an apparatus based on this principle ; it is composed of two equal quantities of the reagent prepared under the same conditions. Above the liquid are two gas chambers of the same volume. * Lum. El, Vol. XXIV. p. 85, 1886. t Lum. EL, Vol. XXXIII. p. 407. \ Bulletin des sciences physiques, Vol. III. p. 149, 1890. 98 PHOTOMETRY. A capillary tube bent twice and fitting closely in rubber stoppers puts into connection the liquid in the two receptacles. After having filled it with liquid, an air bubble is introduced to serve as an index (Fig. 37). The receptacles being opaque, windows of equal dimensions per- mit the illumination of equal surfaces of iodide of nitrogen in each of them. By the aid of the mirrors M, M' inclined at 45 we illuminate one of the windows by the photometric standard, and the other by the radiant to be studied. The index will not remain stationary unless the volumes of nitrogen disengaged in the same time are equal ; that is, unless the win- dows are equally illuminated. Keeping the position of the standard the same, it is sufficient to move the other radiant until this condition is realized, which permits FIG. ST. Lion's Photometric us to apply the law of the squares of the distances. Lion has perfected this elementary apparatus in order to elimi- nate the causes of error. We may refer to Lion's memoir for the description and theory of this photometer, though making the same reservation as for the preceding apparatus. Pupillary Photometer. 60. We know that the diameter of the pupil diminishes as the intensity of the light which strikes the eye increases; the object of this is to protect the eye against the injurious action of too intense luminous excitations. If we knew the diameter of the pupil which corresponds to a given intensity of the luminous pencil penetrating the eye, we should have in this organ a photometer susceptible of considerable precision. For this we ought to be able to measure exactly and rapidly the diameter of the pupil. The pupillary photometer of Gorham * per- mits this. This apparatus (Fig. 38) is composed of a bronze tube 6 cm. long and 4.5 cm. in diameter, closed at one end by a disc which has near its edge small holes arranged in pairs along the radii of the *Lum. J?Z., Vol. XIV. p. 458. PHOTOMETERS. 99 FIG. 38. Pupil Photometer. disc ; the distance between the two holes of any pair varies progres- sively from 1.8 to 9.8 mm. The tube is closed by a cover which is slit along a radius, with so narrow an opening that it allows only the two holes of one pair to be seen at a time ; this cover is movable around the tube, and has an index which indicates the distance between the observed holes. To make a measurement with this apparatus, we look at the source of light through the two holes exposed by the slit in the cover ; we then see two points of light in appearance quite like that of a double star ; the cover is turned until a pair of spots of light is found whose edges seem to touch. The diameter of the pupil is then found to be indicated by the division on the scale. To make photometric measurements it is necessary first to point at the standard of light placed before a white background, next to point at the source of light to be studied, and to move until the spots of light seen with the same position of the cover seem to touch again. Before proceeding to make measurements, the apparatus, that is one's eye, should be standardized, by determining the diameter of the pupil for different luminous intensities, obtained for instance by observing the photometric standard at variable distances. This process is already old. Lambert determined in the last century the variations of the diameter of the pupil by observing at variable distances a circular opening pierced in a shutter and directed toward the sky. He thus obtained the following values, which may give an idea of the elements which are called into play in this phenomenon: Distance of the Eye from the Eadiant. Visual Angle of the Eadiant. Diameters of the Pupa in Lines (2.4 mm.). Distance of the Eye from the Radiant. Visual Angle of the Radiant. Diameters of the Pupil in Lines (2.4 mm.). 1 8.36' 1.14 6 1.26' 2.31 2 4.20' 1.50 7 1.14' 2.53 3 2.53' 1.70 8 1.05' 2.78 4 2. 10' 1.89 9 0.58' 2.89 5 1.44' 2.08 10 0.56' 3.15 100 PHOTOMETRY. Wheatstone's and Masson's Photometers. 61. Photometers may also be constructed based on the duration of luminous sensation. Wheatstone and Masson, in particular, have constructed photometers of this kind. Wheatstone's photometer consists of a polished ball of steel fixed on a disc placed eccentrically on a toothed pinion, which engages with the inner circumference of a toothed wheel. The ball may be moved rapidly by means of a crank which acts upon a series of cogs; if, during the movement, a pencil of light falls on the apparatus, the eye will perceive, in consequence of the reflection on the movable ball, a closed figure composed of epicycloids. It is sufficient to illuminate the apparatus by two radiants to obtain two figures whose equality of luminous intensity is determined by moving either or both of the radiants. Masson* in his photometer uses a disc on which alternately black and white sectors are painted; this dis3 appears uniformly gray when set in rapid rotation, while if it is suddenly illuminated, it seems stationary, and the sectors appear distinctly black and white. Placing the radiants at a sufficient distance the illumination becomes too weak for the sectors to be distinguished, and the disc again appears uniformly gray. The photometric measurement consists in successively moving the two radiants until the disc appears uniformly gray; the intensities of the two radiants com- pared are then proportional to the square of the distances. F. SPECTROPHOTOMETRY. 62. The general problem of photometry, that is, the comparison of differently colored radiants, can only be solved in an approximate manner by the methods previously described. To solve it exactly we must compare the ratios of the intensities of each of the simple rays which compose the light emitted by each radiant. Now this comparison may be effected by the aid of spectrophotometers alone. P>ut the difficulty and length of spectrophotometric measurements interfere with this apparatus ever coming into common use in industrial practice. The description and study of spectrophotometers exceed then the limits of this work. However, to be complete, we shall give from *Ann. de Chim. et de Phys., 3 e sSrie, Vol. XIV. p. 137. PHOTOMETERS. 101 Crova * a cursory glance at the principal apparatus, while referring to the original memoirs for a complete study. 63. Govi t was the first to publish the description of an analyzing photometer. The lights to be compared are received on two rectan- gular prisms placed before the slit, then reflected on an achromatic lens and dispersed by a prism. The two spectra in juxtaposition are received on a strip of glass covered with starch, identical with that of the Foucault photometer. This glass is covered by an opaque screen with a slit, which allows only the light of a single color of the two spectra to pass. Equality of illumination of the two divisions is brought about by suitably varying the distances of the two radiants. Govi also proposed to polarize them at right angles and to equalize the intensity by the rotation of a Nicol analyzer, as Arago had already done in his photometric researches. 64. Later Vierordt $ published an account of a spectrophotometer which he applied to the qualitative analysis of colored substances dissolved in liquids. Vierordt's spectrophotometer is an ordinary spectroscope whose slit is formed on one side by a continuous plate, on the other by a plate identical with the first except that it is cut into two equal parts, each of which is moved by a micrometer screw; thus two slits of unequal width are obtained which give in the spectroscope two superposed spectra of ^different intensities. If the two half-slits receive light of unequal intensity, or, indeed, if one receives light directly, and the other the same light modified bv the absorption which it has undergone in passing through a colored -medium, we may equalize the intensities of the rays of the same wave-length in the two spectra by suitably varying the sizes of the two half-slits; the intensities are then in inverse ratio to the size of the slits. This arrangement is sufficient when the intensities to be com- pared are not very different ; when they are very different, we must enlarge one of the two half-slits a great deal, and the corresponding spectrum becomes more and more impure because of the super- position of rays of different refrangibilities at one and the same point of the spectrum ; the two colors to be compared can then no longer be made identical. In this case, Vierordt used glasses slightly * Ann. de Chim. et de Phys., 5 e sSrie, Vol. XIX. p. 472. t Comptes Rendus, Vol. L. p. 156, 1860. \ Poggendorffs Annalen, Vol. 140, p. 172, 1870. 102 PHOTOMETRY. smoked, which he placed in the path of the more intense light, so as to render the intensity of its spectrum little different from that of the other; equality of intensity is then obtained by a slight variation in the width of the slits. 65. It then becomes necessary to determine for each of the smoked glasses the coefficients of absorption corresponding to vari- ous simple rays. Trannin* has constructed a more convenient pho- tometer. He made use of the phenomenon of the disappearance of the complementary fringes of the two lights polarized at right angles. This principle had already been applied by Babinet, Wild, and by other physicists. The two lights, reflected by two rectangular prisms placed before the two halves of the slit of the spectroscope, are first polarized by a Foucault prism, then traverse a quartz plate parallel to the axis, and finally a Wollaston prism, which gives two images, polarized at right angles, of each half of the slit. The dispersion prism therefore gives four spectra, two of which, polarized at right angles and coming from the two halves of the slit, are partially superpose! in the middle of the field. The insertion of the quartz has i'or its object the production, in the four spectra, of bands whose intensities are complementary in the two spectra polarized at right angles ; they ought, therefore, to disappear in the region where the two spectra are superposed, when we have equalized the intensities of the two spectra at the point considered. We arrive at this result either by varying the distance between the two lights and the instrument or by interposing between the Wollaston prism and the dispersion prism a Fouc.iult prism, which by a suitable rotation produces equality of the two intensities. 66. Glanf has invented a spectrophometer whose construction is analogous to that of Trannin's instrument, but which differs from it in the method adopted for obtaining equality of the intensities of the two contiguous spectra. The slit of the spectroscope is divided into two equal parts by a transverse strip of blackened brass. We obtain thus two spectra separated by an obscure interval. A Wollaston prism placed behind the objective of the collimator doubles the image of each half-slit so as to have, not two, but four spectra polarized two and two at ri^ht angles. For a suitable width of the transverse brass strip the * Journal de Physique, Vol. V. p. 297, 1876. t Wiedemanns Annalen, Vol. I. p. 353, 1877. PHOTOMETERS. 103 lower spectrum of the upper half-slit is tangent to the upper spectrum of the lower half-slit, and we conclude that, by a suitable rotation of a nicol movable on a divided circle, placed between the Wollaston prism and the dispersion prism, we may obtain equality of intensity of the two adjacent monochromatic regions in the two contiguous spectra of the lights compared. Let / x be the intensity of the ray A. of the lower spectrum of the upper half-slit, I 2 that of the same ray in the upper spectrum, % and a 2 the coefficients of diminution due to the refractions and absorptions which the two pencils undergo in the apparatus, and a the angle between the prin- cipal sections of the Nicol pri^m and the Wollaston prism ; we shall have /!<*! cos 2 a = La. 2 bin 2 a. If the intensity of the first ray changes and becomes //, the inten- sity of the other remaining constant, there must be a rotation a 1 to re-establish the equality of the intensities ; we have, then, J/tti cos 2 ' = J 2 a 2 sin 2 a', whence = tanV /! tan 2 In order the better to appreciate the equality of intensity of the two contiguous divisions, we rid ourselves of all extraneous light by means of a slit formed of two plates of blackened brass, which are movable in the focal plane of the telescope, and whose separa- tion is regulated so as to admit only the rays to be compared. But in order that this comparison may be made with precision, the two luminous divisions must be brought into contact without being separated by a line either light or dark. Now the two spectra to be compared have undergone unequal deviation in the direction perpendicular to their length because of the special dispersion which the Wollaston prism has given them. In both, the violet is more deviated than the red, and, as the devia- tions take place for both in opposite directions, exact contact is only obtained for a determinate region of the spectra, in the middle for instance; while toward the violet the two spectra overlap, and toward the red they are separated by a dark interval. However, to obtain contact of the two divisions belonging to any region of the two spectra, we move the slit of the objective of the colli- mator suitably back or forth, which varies the ratio of the width 104 PHOTOMETRY. of the brass strip to the distance of the images of the two half- slits in the Wollaston prism. When this instrument is used to compare two radiants, we should cover one of the half-slits of one rectangular prism, which totally reflects, along the axis of the instrument, the light of one of the sources placed at the side, while that of the other is received directly on the other half-slit. Crova's Spectrophotometer. 67. Crova* has modified Glan's spectrophotometer so as to make it more precise. Following is the description of the apparatus. The lamp to be studied, L' (Fig. 39), is placed in front of a circular opening in a rectangular box, blackened within, and illu- minates the lower part of the slit F, whose width may be regulated FIG. 39. Crova's Spectrophotometer. at pleasure by means of the screw V. The light emitted by the standard L, which has traversed a nicol N, movable on its grad- uated circle CO, is received through a lateral opening in the box, on a prism of total reflection P, which covers only the upper half of the slit F. The rays emanating from the two sources, after passing through the slit F, traverse a fixed Nicol analyzer N', and a system of prisms P' forming a direct vision spectroscope, and are displayed in two superposed and contiguous spectra. These spectra are examined by means of an eyepiece Z", at the extremity of a tube M", which can be moved laterally by means of a rack and pinion F 7 , so as to traverse the whole field of the spec- trum. We rid ourselves of all light, other than the radiations which we wish to compare, by means of a slit F 1 between t\vo blackened * Ann. de Chim. et de Phys., 6* serie, Vol. XIX. p. 495 and Vol. XXIX. p. 656. PHOTOMETERS. 105 brass plates moving in the focal plane of the telescope VI", and whose separation is governed at will. In this apparatus we annul the elliptical polarization due to total reflection by employing a double total reflection prism. That the instrument may serve for the photometric study of the rays of the spectrum, and especially that it may be calibrated, a microm- eter M is placed at the side as in all direct-vision spectroscopes. VVITIRSXTT CHAPTER III. PHOTOMETRIC STANDARDS. Introduction. 68. The first photometric standard was the candle which Bouguer constantly employed in his researches. As long as there were only luminants of low power to be measured, the candle sufficed as a unit of comparison, no account having been taken, to be sure, of constancy and comparability. For photometric measurements of the illuminating power of gas- lights, Dumas and Regnault saw the necessity of a standard at the same time more constant, more comparable with itself, and more intense. They then adopted the carcel lamp, which gave in their hands exact results and which, since then, has been generally employed in France for all industrial photometric measurements. In France, Giroud, and in England, Methven, sought to represent the standard of light by means of a flame burning ordinary illuminating gas, such as is furnished for consumption ; but these standards depend in a great measure on the composition of the gas. Vernon-Harcourt of London sought to produce a gas of constant composition by utilizing, as a combustible, air carburetted by vola- tile carburets of hydrogen extracted from petroleum, principally by pentane. The burner used is a candle-burner of well-defined dimen- sions, and the flow of gas is automatically regulated. There should be mentioned also among the standards of light produced by combustion, the ascetate of amyl lamp of von Hefner- Alteneck, which gives a light of very satisfactory constancy, but of too slight intensity. In this lamp of free combustion, the wick is immersed in ascetate of amyl, which gives better results than other hydrocarbons, benzine and ligroin* for instance. In petroleum lamps which are universally used, the rise of oil in the wick takes place solely by capillary action ; considerable varia- *"That part of petroleum which has a boiling-point between 90 and 120 C." Cent. Dictionary. 106 PHOTOMETRIC STANDARDS. 107 tion results in the intensity according to the height of the liquid in the reservoir. Further, the composition of commercial petroleum is far from being constant. In order that the photometric standard furnished by the preced- ing apparatus may be utilizable, the flame must always be the same, the combustible and supporter of combustion must have a constant composition, and combustion must take place under invariable con- ditions. Now flame standards are sensitive in a great measure to every modification in the state of the supporter of combustion. Thus a candle and a carcel lamp depart very rapidly from the normal condition when they are put in a somewhat small room con- taining several observers. Further, the illuminating power of a luminous body depends on its temperature; the former increases very rapidly with the latter, so that the higher the temperature of a luminous body is raised, the more necessary is it to obtain constancy in it, without which the luminous intensity would be essentially variable. Now, in a flame, constancy of temperature is not easy to realize, for it requires that the mixture of combustible and supporter of combustion should always be made under identical conditions. If this mixture is not perfect and invariable, the temperature varies, and the brightness even more. Finally, a flame is always transparent, and the quantity of light emitted varies with the degree of transparency. In order that a flame may emit constant luminous radiations, it is not sufficient for the temperature to be invariable ; it is necessary in addition that the transparency of the flame and its thickness undergo no change. To furnish a satisfactory unit of light, a flame should then satisfy an aggregation of conditions quite difficult to realize com- pletely. These are the difficulties which determined the Inter- national Commission on Electrical Units to reject definitely, as the absolute standard, standards of combustion, and to adopt the platinum standard proposed by Violle. The advantages of a standard of light based on the incandescence of a body raised to a high temperature, for instance to the tempera- ture of fusion of platinum, have been recognized for a long time by all physicists. As early as 1844 Draper indicated the possibility of taking as unity the light emitted by platinum wire made incan- descent by the passage of an electrical current, and later, in 1859, Zoellner also conceived the same idea. It was taken up again in 1878 by Schwendler, in Calcutta, who made numerous attempts 108 PHOTOMETRY. with apparatus constructed with a view to realizing this photo- metric standard. Schwendler's platinum standard is excellent in theory, but cannot give satisfactory practical results, because of the modifications which platinum undergoes as a consequence of slightly prolonged incandescence. Under the action of the electrical current con- tinuous modifications are produced in the platinum wire to which changes in electrical resistance correspond and, consequently, with the same current, changes in temperature. Incandescent lamps, as they are now made, are free from a part only of these defects ; the luminous intensity for a constant current varies, although very slowly ; but the energy spent in the lamp is divided differently, according to the nature of the carbon, into calorific energy and luminous energy. At the International Congress of Electricians in 1881, Violle proposed as the absolute standard of light the light emitted normally by 1 sq. cm. of platinum raised to its fusion point and about to solidify. The phenomenon here employed has the advantage of being constant and susceptible of being always exactly reproduced. A liquid metal which is on the point of solidifying, and which is furthermore unalterable, like platinum, constitutes a body of fixed temperature. The temperature remains in fact invariable as long as any part of the mass remains liquid. If this metal is unalterable, like platinum, it will always have the same emissive power. With a given surface, it will always emit the same quantity of light. The quality of this light depends on the temperature; platinum, being the most refractory of ordinary metals, will be the one which, at its point of fusion, will give the whitest light. As a consequence of the researches undertaken by Violle, which have demonstrated the exactness of the arguments by which he supported his proposition before the congress, the International Commission on Electrical Units, in session at Paris in 1883, definitely adopted as the absolute standard of white light the standard proposed by this French savant. The Absolute Standard and Secondary Standards. 69. Before studying in detail the principal photometric stan- dards, we must examine carefully the relative importance of an absolute standard and secondary standards. The difference between these two classes of standards is analogous to that which exists, PHOTOMETRIC STANDARDS. 109 for instance, between the original meter and the original kilogram in indium-platinum, and their ordinary copies in iron, brass, or wood. The original meter and kilogram were constructed according to their definition with all the exactness that modern methods afford, and they have been kept in such a way as to guarantee perfect invariability. Since then national standards have been established which serve in each country for the comparison of the usual units of commerce and industry. It should be the same with the unit of light, always with one difference. The prototypes of the metric system may be materially represented, and this representation is invariable at a given place. It cannot be the same with the absolute standard of light or with secondary standards ; they must be constructed each time it is desired to use them, and to support them it is necessary to spend a certain quantity of energy. The value of the standard of light depends on the energy spent and on the conditions under which this transformation of energy is effected. The only thing which may be done is to employ appa- ratus of definite dimensions, giving, under fixed conditions, the same luminous intensity. The absolute standard and secondary standards should be as nearly as possible independent of the dangers mentioned above; this condition is necessary for the absolute standard ; it renders its construction and reproduction difficult, so that its employment in industrial practice would not be dreamed of. Thus the employment of secondary standards becomes necessary. It is sufficient, in fact, to construct the absolute standard in a fixed place, and to make all the comparisons of secondary standards under the most varied con- ditions of working. The choice of an absolute standard being made judiciously, we may afterwards in secondary standards profit by all the improvements and simplifications taught by prolonged use, without introducing confusion into the measurements, since the value of secondary standards is always expressed as a function of the absolute standard. We employ as a unit of comparison the standard whose luminous intensity gives the most facility or pre- cision in the experiments, according to the nature of the radiants to be compared. These secondary standards are then multiples and submultiples of the absolute standard, in the same way as in the metric system the kilometer is a multiple and the centimeter a sub- multiple of the meter. 110 PHOTOMETRY. It suffices if the secondary standard is of sufficient constancy for current practice. While we may reasonably require of the abso- lute standard a constancy of % per cent, we may be satisfied with the secondary standard if its constancy proves to be within 2 per cent. These considerations show, indeed, that a uniform secondary standard is not necessary, and, in certain cases, would be even dis- advantageous, since the known relation of each to the absolute standard brings about complete unity in photometric measurements. The Mechanical Equivalent of the Unit of Light. 70. The standard of light being defined, it is interesting to investigate the quantity of energy in the luminous rays which it emits. This quantity is easy enough to determine. It is enough to measure by an air thermometer the energy corresponding to the totality of the rays emitted by the radiant, then, by a thermo-electric pile, to measure the ratio between the energy of the luminous rays and that of all the rays. A simple multiplication then gives the energy corresponding to the luminous rays or the mechanical equivalent of the light emitted by this radiant. This is the process which Tumlirz* employed to determine the mechanical equivalent of the light emitted by the flame of the Hefner ascetate of amyl standard. He found k = 0.00361 small calorie per second, or transforming, k = 151,500 ergs per second, which corresponds to the electrical work of a current of 0.1226 amperes in a conductor of 1 ohm. This may also be expressed as follows : if the flame of the asce- tate of amyl lamp is placed at a distance of 1 m. from an element of surface 1 cm. square, so placed that its normal is horizontal and passes through the center of the flame, the quantity of light which strikes this element of surface corresponds to a quantity of heat of 0.000000361 small calorie per second or 15.15 ergs. If the eye replaces the element of surface and if we suppose that the pupil has an opening of 3 mm., the quantity of light which penetrates the eye corresponds to 1.07 ergs per second ; this work * Wifdemanns Annalen,Vo\. XXXVIII. p. 640. PHOTOMETRIC STANDARDS. Ill would require a year and 89 days to raise the temperature of a gram of water one degree C. The value of the mechanical equivalent of the ascetate of amyl standard being determined, a simple photometric comparison allows us to find the mechanical equivalent of other standards of light. Tumlirz found in this manner the following value for the German candle : Jc = 0.00447 small calorie = 187,900 ergs. THE CARCEL STANDARD. 71. The carcel lamp is a simple modification of the Argand lamp ; we know that in 1787 its Genevese maker produced a revo- lution in illumination, by replacing the flat wick burning openly in the air by a round wick giving passage through it and around its edge to a double current of air, produced by a metal chimney placed above the flame. Soon this metal chimney was replaced by a glass tube having at the top of the flame a constriction which forces the air into closer contact with the flame and which thus brings about complete combustion. In 1800, Carcel made an important modification of the Argand lamp, giving it a very regular feed of oil. In this modification the oil reservoir is placed in the base of the lamp and the oil is raised to the level of the top of the wick by means of clock-work which oper- ates two small pumps in the standard. The quantity of oil raised should be greater than that which is required for combustion, and the excess falls back to the reservoir ; the wick, constantly wet with oil at the point where combustion is taking place, is charred very slowly and gives an almost constant light. Since the mechanism is apt to get out of order, a regulating lamp is preferably employed, in which the pressure of a spring on a piston produces the same effect as the clock-work ; the flow of oil is ren- dered sensibly constant by means of a small tube, fixed to the piston, in which there fits a fixed regulating rod which offers less obstruc- tion in proportion as the piston is lower and the pressure of the spring less. At the time of their photometric studies relative to the illumina- tion of light-houses, Arago and Fresnel employed the oil lamp. Fresnel showed that by using certain precautions great constancy may be obtained within certain limits. It is well to remember the following interesting detail to show what care should be used in pho- 112 PHOTOMETRY. tometric measurements. Fresnel insisted, himself, on cleaning and caring for the lamps which he used ; he took, further, the greatest precautions to insure the constancy and comparability of this stan- dard. The carcel lamp was next adopted by Dumas and Eegnault for the photometric tests of the gas illumination of Paris. The good results obtained on this occasion and the authority of the two savants led to a general adoption of this unit of light by the gas companies in France. The conclusions of Dumas and Kegnault were published after a long series of researches made in the municipal laboratory of Paris by Audoin and Berard* ; these last have shown the conditions which must be realized to insure the constancy and comparability of the carcel standard. 72. The luminous intensity of the carcel lamp depends on many circumstances of which the principal are the height of the wick, its nature, and the height of the constriction of the glass above the level of the wick. Audoin and Berard investigated the influence of each of these conditions on the intensity and consumption of the carcel burner. TABLE I. FINE WICK. MEDIUM WICK. COARSE WICK. Height of the Wick. Consump- tion of Oil per Hour. Consumption of Gas calcu- lated to equal the Carcel burning 42 gr. Consump- tion of Oil per Hour. Consumption of Gas calcu- lated to equal the Carcel burning 42 gr. Consump- tion of Oil per Hour. Consumption of Gas calcu- lated to equal the Carcel burning 42 gr. mm. grams. liters. grams. liters. grams. liters. 4 27 96 30 155 32 99 6 33 175 36 193 36 159 8 38 196 42 185 42 192 10 40 190 42 200 45 194 12 35 170 40 193 48 212 14 38 177 40 51 216 16 36 180 45 186 48 189 18 31 153 42 192 Table I. shows the results of tests made with various heights of the wick; Table II. shows the results of tests made with a constant * Ann. de Chim. et de Phys. 3 e s6rie, Vol. LXV. PHOTOMETRIC STANDARDS. US height of wick of 7 mm., but varying the position of the chimney. The relative luminous intensity is indicated by the number of liters of gas consumed by the gas-burner to give an equal light. TABLE II. Height of the Bend above the Level of the Wick. FINE WICK. MEDIUM WICK. COARSE WICK. Consump- tion of Oil per Hour. Consumption of Gas calcu- lated to equal the Carcel burning 42 gr. Consump- tion of Oil per Hour. Consumption of Gas calcu- lated to equal the Carcel burning 42 gr. Consump- tion of Oil per Hour. Consumption of Gas calcu- lated to equaL the Carcel burning 42 gr. mrn. - 2 grains. 18 liters. 24 grams. 18 liters. 11 grams. 15 liters. 23 + 3 25 63 21 57 27 7 36 187 39 161 48 175 12 39 199 42 200 50 186 19 42 151 45 175 51 164 24 46 315 45 161 54 140 29 flares. .... 51 133 / The preceding figures show that the intensity of the carcel burner depends : 1. On the height of the wick ; as this increases, the consump- tion of oil and the luminous intensity increase up to a height of 10 mm. for the medium wick ; above this limit the two quantities diminish. 2. On the wick adopted ; the medium wick is the best, for it gives the greatest luminous intensity for an equal consumption. 3. On the height of the constriction of the glass chimney above the level of the wick ; the elevation of the constriction tends to increase the consumption of oil in an always increasing proportion, but there exists a height of the chimney's neck which corresponds to a maximum of illuminating power. Thus with the medium wick in these tests, the height of the bend should be 7 mm. above the level of the wick. Dimensions and Working Conditions of the Carcel Lamp. 73. The dimensions and working conditions of the carcel stand- ard, as given by Dumas and Regnault in their practical instructions for gas testing, are given below (Fig. 40). PHOTOMETRY. Extreme diameter of the burner 23.5 mm. Interior diameter (for the interior current of air) . . 17.0 Diameter of exterior current of air 45.5 Total height of the glass chimney 290.0 Distance of the bend from the base of the chimney . . 61.0 Exterior diameter at the bend 47.0 Exterior diameter at the top of the chimney .... 34.0 Mean thickness of the glass 2.0 The wick adopted is the medium one, called the light-house wick ; the strand is composed of 75 threads and weighs 3.6 grams per decimeter. The wicks should be kept in a dry place, or preferably in a box with a double bottom containing unslaked lime. The carcel lamp burns well-purified rape-seed oil. According to Crova, the composition of the rape-seed oil which is used in these lamps is apt to undergo only insignificant variations, for it is furnished by the grain of a particular vegetable, and its purity is more easy to control than that of other combustibles, such as stearic acid, sperma- ceti, parafnne, petroleum, and gas. This oil is purified by adding a small quantity of sulphuric acid, which coagulates the mucilage which it natu- rally contains and renders it more limped and more fluid. The opinion of Crova seems somewhat optimis- tic, although its author has had occasion to employ the carcel lamp frequently in the course of his ex- cellent photometric work. It should be remarked, in fact, that vegetable products are rarely of con- stant composition and are easily affected by exter- nal causes and even by the action of time alone, and that the process of manufacture is not abso- lutely definite. FIG. 40. Burner of the Carcel Lamp. 74. For any combustible there is in general no definite relation between the quantity of material burned and the light produced ; but adopting the dimensions given above for the burner and the chimney of the carcel lamp, and using a medium wick, it is noticed that the quantity of light increases in direct proportion to the consumption of oil, when this consumption PHOTOMETRIC STANDARDS. 115 is in the neighborhood of 42 grams per hour ; however, the con- sumption should not be below 38 grams, nor above 46 grams, for this proportion to hold good. Two lamps having the same diameter of wick and the same capacity may differ in their consumption of oil and their illuminating power ; further, it is known that the temperature, the movement of the air, the duration of the illumination, and the fullness of the lamp, have an influence on the quantity consumed. We should then, before using the carcel lamp as a standard, submit it to a series of tests to obtain the exact conditions under which it should be placed to obtain a nearly constant consumption. These conditions obtained, we may proceed to definite photo- metric measurements. For each experiment we should insert a new wick which is trimmed even with the wick-holder; next the lamp is filled up to the beginning of the gallery, it is afterward lighted, keeping the wick at first 5 or 6 mm. high, and then the chimney is put on. The consumption of oil is regulated by raising the wick to a height of 10 mm. and the chimney so that the bend may be at a height of 7 mm. above the level of the wick. To easily realize these conditions, we make the lower point of the small contrivance which is fitted to the wick-holder level with the wick itself, and the upper point level with a diamond scratch on the neck of the chimney. The consumption and intensity increase slowly during the first half-hour, because of the heating of the burner; at the end of this time a constant state is established which lasts more than an hour ; it is during this period that the photometric observations are made ; then the consumption and intensity begin to decrease slowly in proportion as the wick becomes charred. 75. The lamp should consume 42 grams of oil per hour ; when the consumption falls below 38 grams or rises above 46 grams, the tests should be rejected. When the consumption is maintained between these limits, the luminous intensity is reduced by a simple proportion to that which corresponds exactly to 42 grams per hour. To regulate th consumption of the lamp, we suspend it at the end of one of the arms of a balance having on the other arm a coun- terweight ; equilibrium being obtained at any given time, a weight of 10 grams is placed on the side of the lamp ; when this weight of oil is consumed, the balance returns to its position of equilibrium ; now the point of the balance has a notch which at the moment of equi- 116 PH TOMETR Y. librium causes the fall of a hammer; this, striking a bell, notifies the experimenter, who reads on a seconds counter the time necessary for the burning of 10 grains of oil. The apparatus was constructed by Deleuil, who gave it a very practical form. (Fig. 54, p. 165.) The normal consumption of the carcel standard being 42 grams per hour, it requires 14 minutes and 17 seconds to burn 10 grams. The seconds counter permits the determination in each experiment of the rate per hour at which the lamp consumes oil and indicates whether we are within the prescribed limits. If, for instance, the counter indicates 15 minutes 30 seconds, the proportion 10:15.5::z:60 gives immediately 38.7 grams as the rate per hour of consumption of oil. The carcel standard is only comparable with itself on condition that we adopt the dimensions indicated above. In the carcel lamp, the layer which emits the light has the form of a hollow cylinder included between two cylindrical layers, one outside, the other inside, where the combustion of hydrocarbons takes place at a very high temperature without the deposit of carbon. In the interme- diate layer which radiates the light, the hydrocarbons are disso- ciated with the formation of solid incandescent carbon ; this last is- raised to a temperature higher in proportion as the temperature of the two non-luminous layers between which it is found is higher, which happens when the draught of the chimney is very active. This shows well the importance of an exact determination of the conditions of combustion. Practical Value of the Carcel Lamp. 76. Opinions are much divided as to the practical value of the carcel standard; while French engineers think its qualities unri- valled, in other countries other photometric standards are used. In connection with this, the discussions which took place at the Inter- national Congress of Electricians, in 1881, and at the International Conference of 1882, are very interesting. The French representatives, Dumas, Allard, Crova, etc., all in- sisted on the advantages of the carcel lamp, advantages scarcely recognized by foreign savants, who put this standard on a par with the candle. The numerous experiments of Crova showed that two very differ- PHOTOMETRIC STANDARDS, 117 ent carcel lamps, compared within an hour, give indications whose variations amount to from 2 per cent to 3 per cent at most. According to Leblanc*, the employees charged with testing the gas at the municipal bureau of Paris easily acquire such experience that they regulate the consumption of the oil very exactly between 41 and 42 grams per hour. It follows, from the measurements made daily in this bureau, that the carcel lamp, well cared for and care- fully manipulated, can give good results, quite comparable with one another. However, this agreement does not happen with lamps, wicks, and rape-seed oil of different origins ; it is probably to this that we must attribute the great differences which have been several times found to exist by foreign engineers who have used the carcel lamp in their photometric comparisons, but without following exactly the very minute directions given by Dumas and Regiiault. It is of the greatest importance to observe exactly all the pre- cautions mentioned by these two scientists; then only may we have results truly comparable to those of other observers, working under analogous conditions. Leblanc recommends the use of two lamps, which are used on alternate days ; when a lamp remains unused for several days, the oil thickens and the mechanism gets out of order. We have considered so far only the opinions of those who favor the employment of the carcel lamp, after having used it for a long time. However, we must not be blind to the fact that this standard has also serious inconveniences. To give an idea of them, we cannot do better than to cite the fol- lowing passage from a communication of Hartley f to the British Association of Gas Managers, in 1880 : "The very great number of tests that I made in 1867 with a carcel lamp does not encourage me to give credit to the indications of any lamp in which vegetable oil is used. I say vegetable oil because some recent experiments with lamps burning paraffine oil have shown great uniformity in their illuminating power. "The objections which I have to standard lamps are that they must be kept in a state of perfect cleanliness ; the wick must be renewed very often, if not each time the lamp is used (this last point is essential with the carcel lamp); the wick as well as the * ProcZs-verbaux de la Conference Internationale, 1882, p. 145. t Journal des usines a gaz, 1882. 118 PHO TONE TR Y. chimney must be adjusted with the greatest care and exactness, and finally, when all this has been done, there is no certainty that the quantity of oil consumed will not be greatly in excess of the regula- tion quantity. " This variation in the consumption would have no effect if, as my experiments have shown me, the quantity of light emitted did not often increase in a much more rapid proportion than the consump- tion of oil. It is, furthermore, very difficult to keep the consumption of the lamp as low as the regulation rate." In spite of all the fault that may be found with the carcel lamp, it has remained, nevertheless, a practical standard of light which has rendered great service in industrial photometric comparisons ; its intensity and color are about the same as those of the gas-burn- ers generally employed. In the comparison of arc lights, the question becomes compli- cated, for the flame of the carcel lamp is" still too red to render insensible the differences of color which enter so largely into pho- tometric comparisons. CANDLES. 77. The candle, although giving poorer results than the other standards of light with respect to the constancy of the light emitted, has enjoyed up to the present the greatest favor. Petroleum lamps and other oil lamps furnish a quantity of light which depends on the dimensions of the wick, than which there is nothing more varied, while there exists a certain uniformity in the composition and dimensions of the candles which commerce pro- duces in such great quantity. Hence the employment of this radi- ant as the usual photometric standard. Practice has recognized the use of four different candles furnish- ing, even under identical conditions, unequal quantities of light. It is necessary, then, when speaking of candles, to specify the one meant; this is a precaution which unfortunately has not been observed. These four kinds of candles are : 1. The Stearine Star candle, which is used in France along with the carcel lamp. 2. The London Standard Spermaceti candle, which is used in England and the United States. PHOTOMETRIC STANDARDS. 119 o. The candle of the Union of German gas-men, " Vereinskerze," a paraffine candle, which is much employed in Germany and Austro- Hungary. 4. The Munich Stearine candle, in form slightly conical, which is in use in Germany along with the paraffine candle. There should be added also the decimal candle denned by the Congress of Electricians, in 1889, as the twentieth part of the abso- lute platinum standard. Combustion of the Candle. 78. The luminous intensities of these candles, burning under normal conditions, have been determined many times by a great number of observers who have compared them with one another or with the carcel lamp. The values obtained are very different ; it is the same with the conclusions relative to the variability of the luminous power of the candle. Thus while Schwendler says that he has found variations of from 40 to 50 per cent in the intensity of an English candle, Hugo Krtiss says that, taking certain precautions, one may easily succeed in keeping the light emitted by the flame of a paraffine candle con- stant within 5 per cent. The luminous intensity of the flame of a candle, whatever be the nature of the combustible of which it is made, depends on the form and nature of the wick, which vary greatly with the mode of manufacture. The wick is generally formed of many strands of cotton, braide;! and saturated beforehand with a solution of boric acid. When the candle is lighted, the wax melts, rises by capillarity in the wick, and is decomposed into products rich in hydrocarbons which burn, and into carbon which is precipitated in a solid and finely divided state in the middle of the flame. The gaseous envelope, in contact with the air, burns completely without precipitation of carbon, at a very high temperature and without sensible emission of light. The temperature of this layer is very high, and certainly approaches, according to Crova, that of the fusion of platinum. The carbon precipitated in the middle of the flame at a very high temperature undergoes combustion, which is produced with a great elevation of temperature, accompanied by a strong emission of light by the incandescent carbon. 120 PHOTOMETRY. The axis of the flame, relatively cold, is composed of pyrogenous products not yet dissociated; it is in this axial part and in the luminous envelope that the upper part of the wick is found which undergoes gradual carbonization ; as it bends over, it approaches the outer part, where it is completely burned ; the boric acid which the wick contains then melts and vitrifies the ashes of the cotton in the form of small globules, whose weight bends the wick outside the flame, and thus brings about its complete combustion. The wick, then, undergoes continual changes in form and position ; hence the variations in the state of the flame which is unequally chilled and modified in its form: this may be proved by placing before a Foucault photometer a carcel lamp and a candle. If the lamp is so regulated as to insure the greatest possible constancy, we may follow, on the photometric screen, the variations of intensity of the candle, and determine their agreement with the corresponding form and position of the wick. The influence of torsion in the wick is also very sensible ; as far as possible, the wick, quite regularly braided and made of a well- determined number of strands, should be placed without torsion in the middle of the candle ; if this condition is not rigidly complied with, the curvature of the wick in the flame changes continually in direction, sometimes even abruptly ; there then result very consid- erable variations in the luminous intensity of the flame. The movement of the air exerts a very great influence on the light of the candle ; if the air is even slightly stirred, the variations are very great. If, to avoid these disturbances, the candle is enclosed in a black- ened box, having openings planned to remove the products of com- bustion and to admit fresh air, the ascending movement of the air in the box also exerts a very notable influence on the composition and intensity of the light emitted. The more rapid the movement, the more the exterior non-lumi- nous envelope of the flame develops, the higher also the temperature of the middle layer, which radiates the light, rises, and its mass becomes less, so that as the draught increases, the reddish yellow of the flame becomes more and more white and less and less bright. This effect may be shown by exaggerating it; it is sufficient to surround the candle with a large glass tube acting as a ch'imney, whose draught produces in a more marked manner the effects indi- cated above. It is, then, necessary to place the photometric candle in air perfectly quiet and free ; but these are conditions difficult to PHOTOMETRIC STANDARDS. 121 realize in industrial practice. Variations of the temperature of the photometric chamber and of the barometric pressure modify the conditions of combustion of the candle : consequently they have an influence on its luminous intensity. In order to become as independent as possible of the variations indicated above, the quantity of material burned by each candle per hour was specified. However, it was not long before it was noticed that this condition is not sufficient in all cases, and there was then added the height which the flame must have during the measurements in order that the luminous intensity may be constant. The Star Candle. 79. The French Star candle burns 10 grams of material per liour. Peclet, in 1830, compared the first candles made by de Milly ; he found that they gave a light whose intensity was equal to }- carcel. Candles of this quality are no longer to be found ; the best candles made in France do not equal more than -J- carcel. According to Monnier, the employment of the Star candle as a photometric unit requires not only a consumption of 10 grams per hour, but a height of flame of 52.4 mm. These candles corne 5 or 6 to the package. The candles with 5 in a package weigh 100 grams each; their dimensions are: total length, 306 mm. ; length of cylindrical part, 290 mm. ; diameter above, 20 mm. ; diameter below, 22 mm. ; the wick is composed of 81 threads. The candles with 6 in a package weigh 83.3 grams ; their dimen- sions are : total length, 274 mm. ; length of cylindrical part, 258 mm. ; diameter above, 20 mm. ; diameter below, 21.5 mm. ; the wick has 81 threads. The comparisons of Star candles with other candles not being numerous on account of their comparatively small employment, we shall give immediately the most probable values of this standard of light as a function of the normal carcel lamp. Monnier found the following mean values. A Star candle equals 0.136 carcel with a mean consumption of 10 grams per hour, and 0.136 carcel also with a height of flame of 52.2 mm. For candles with 6 in a package, the corresponding values are 0.131 and 0.132 carcel. In the same way 1 normal carcel equals 7.4 candles of 5 to the package, or 7.6 candles, 6 to the package, taking as the normal candle that which consumes 10 grams of stearine per hour, or that which gives a flame 52.5 mm. in height. 122 PHO TOMETB Y. The English Candle. 80. The English photometric candle is the spermaceti candle, G to the pound, burning 2 grains of material per minute, or 120 grains (7.776 grams) per hour. Schwendler says 8.26 grams. The dimensions of the candle are : length, 252 mm. ; diameter at top, 20 mm. ; at bottom, 22.5 mm. ; mean weight, 75.7 grams. When the real consumption of the candle differs from this figure, and is between 114 and 126 grains per hour, we assume that the illuminating power is proportional to the consumption, and cor- rection is made by means of a simple proportion. The wick is made of three strands of cotton, each containing from 18 to 21 threads, according to the brand. The height of flame adopted is 45 mm. The composition and purity of spermaceti are liable to considerable variation, according to the source and method of refining. Thus Heisch and Hartley mention the fact, with the proof, that spermaceti candles now give more light for the same weight of matter burned than formerly. This is due to small improvements in the wicks or to progress in the treatment of spermaceti. The German Candle (Vereinskerze). 81. The German Association of Gas and Water Industries adopted in 1868 as photometric candle a paraffine candle of 6 to the pound, having a uniform diameter of 20 mm. ; its length is 314 mm., and its weight 83.6 grams. The melting-point of the paraffine employed is 55 C. The wick is made of a twist of 25 threads of cotton ; a meter of wick weighs 668 mg. The illuminating power of the candle depends on the height of the flame ; unity corresponds to a flame 50 mm. high. The melting-point of paraffine is quite variable, and oscillates between 55 and 65 ; it may even reach 80, or fall to 44. These variations in the melting-point oblige the manufacturers to add, in certain cases, from 10 to 15 per cent of stearine. It is necessary then, in order to have a constant candle, to be sure that its com- position corresponds closely to the conditions of purity mentioned above. The Munich Candle. 82. The Munich candle conforms to the type of candles speci- fied in the contract made between the city of Munich and the gas PHOTOMETRIC STANDARDS. 123 company. They are stearine candles; their form is slightly coni- cal; they are 20.5 mm. in diameter at the top, 23 mm. at the base, 31 cm. long, and weigh 108.9 grams on the average; the wick is made of 50 threads. They should consume 10.2 grams to 10.6 grams of stearine per hour, without smoking and without requiring snuffing; the height of the flame is 56 mm. Variations in the Luminous Intensity of the Candle -with the Height of the Flame and the Consumption of Combustible Material. 83. The consumption of the candle is not sufficient to characterize its luminous intensity ; the height of the flame should also be indi- cated. The employment of candles requires the maintenance of the flame at its normal height ; this result is obtained by snuffing the wick at intervals sufficiently close for the flame to keep its normal height during the time of measurements ; for the variations of this normal height are exceedingly slow when the wick has attained its normal state soon after having been snuffed. As doing this produces a perturbation in the combustion of the candle, it would be preferable to wait until the flame reaches its normal height; but the delay would in general be too long, and thus much time would be lost, the normal height adopted for candles not corresponding exactly to the height of the free flame. As an example we give in the following table* the results found by Kruss with a certain number of candles : MUNICH STEARINE CANDLES. Prescribed Height, 52 mm. Limits of the Height of the Flame. Mean Height of Flame. Mean Devia- tion from the Mean. Sum of the Successive Va- riations in the Height of the Flame. No. 1 53 to 60 mm 55 09 mm 4- 1 07 58 mm. No. 2 51 " 57 " 54 2 " + 1.02 50 " No. 3 51 " 59 " 55.15 " + 1.27 49 " No. 4 .... 49 " 54 " 50 65 " + 0.93 41 " Total or Mean . . 49 to 60 mm. 54.0 mm. 1.98 198 mm. * Journal fur Gasbeleuchtung, 1883, p. 511. 124 PHOTOMETRY. GERMAN CANDLES (VEREINSKERZE). Prescribed Height, 50 mm. Limits of the Height of the Flame. Mean Height of Flame. Mean Devia- tion from the Mean. Sum of the Successive Va- riations in the Height of the Flame. No. 1 51 to 63 min. 54.0 mm. 1.35 63mm. No 2 .... 49 " 56 " 52.5 " 1.52 61 " No 3 47 " 55 " 50.8 " 1.62 62 " No. 4 60 *' 60 " 55.3 " 1.73 90 " Total or mean . . 47 to 63 mm. 53.1 mm. 1.98 276 mm. ENGLISH SPERMACETI CANDLES. Prescribed Height, 44 mm. Limits of the Height of the Flame. Mean Height of Flame. Mean Devia- tion from the Mean. Sum of the Successive Va- riations in the Height of the Flame. No 1 46 to 52 mm. 49.8 mm. 1.20 36 mm. No 2 ... 46 " 50 " 47.5 " 0.92 41 " No 3 .... 46 " 50 " 47.8 " 0.75 39 " No 4 . 44 " 49 " 45.5 " 0.83 41 " Total or mean . . 44 to 52 mm. 47.67 mm. 1.57 157 mm. These results show the differences which exist between the prescribed height of flame and that which is obtained in reality ; for stearine candles, the most frequent height of flame is between 54 and 56 mm., for paraffine candles between 52 and 54 mm., and for spermaceti candles between 47 and 48 mm. The figures in the first column show also that the spermaceti candles differ less from one another than the others ; the figures in the fourth column give, on the contrary, information as to the amount of the variations of the height of the flame and its regu- larity. Thus it is seen that the English spermaceti candle is much superior to the two others, as to the regularity and small amount of variations of each candle. Certain measurements made at the electro-technic station of Munich, under the direction of Voit, confirm Kruss's conclusions. PHOTOMETRIC STANDARDS. 125 These conclusions clearly show that it is necessary to snuff the wick to obtain the normal height of flame. We also give the results obtained by many observers concerning the mean values and the variations of the height of the flame of different candles. MEAN HEIGHTS OF THE FLAME (IN MM.). Candle. Eudorff. Schiele. German Commission. Kruss. Monnier. Voit. Stearine . . . 56.0 50.3 60.8 54.0 55.0 59.3 Paraffine . . . 50.0 50.0 51.2 53.1 50.8 60.4 Spermaceti . . 52.2 52.0 47.7 46.0 44.8 VARIATIONS IN THE HEIGHT OF THE FLAME (PER CENT). Candle. Kudorff. Schiele. German Commission. Kruss. Voit. Stearine ..... Paraffine 5% 8 8% 20 350/ 35 20% 30 5% 4 Spermaceti .... 7 17 17 3 Some measurements were made at the electro-technic station of Munich to determine the variation of luminous intensity with the height of the flame ; and, further, an attempt was made to express this luminous intensity as a function of the height H, by the formula T * T^TT !=. a + oH. The results obtained are given below ; they are very interesting, but the measurements are not numerous enough to draw from them absolute conclusions. Candle. Height of Flame. Number of Measurements. Formula Expressing the Luminous Intensity. Munich . . . 47-55 42-62 87 149 7 = 0.0068 + 0.0192 H 0.035 7- 0.0120 + 0.0190 77 0.064 German . . . 39-53 42-57 197 138 7 = - 0.0300 + 0.0206 77 0.058 7 = 0.0350 + 0.0193 77 0.043 English . . . 32-52 32-49 119 81 1= 0.0077 + 0.0223 77 0.050 7 = 0.0121 + 0.0222 77 0.082 126 PHOTOMETRY. Measurement of the Height of the Flame. 84. The height of the flame being so important an element, it should be possible to measure it easily. Direct measurement of the height of the flame by means of a pair of compasses is scarcely practicable, because of the proximity of the observer and contact of the measuring instrument. The employment of the cathetometer gives excellent results j but this instrument is reserved for laboratory work of great precision. The height may be measured by placing a divided scale behind the candle and observing it with a telescope. On this principle, Krtiss has constructed the following apparatus * which gives good results (Fig. 41). FIG. 41. Optical Scale for Measuring the Height of the Flame. At one of the ends of the tube A is the achromatic objective B, while the other end is fitted with a glass scale C. The distance from the center H of the objective to the divided scale should be equal to twice the focal length of the objective ; the longitudinal movement of A is governed by the screw a, and the vertical movement of the glass scale by the screw b. To make a measurement, the apparatus is so placed that its * Journal fur Gasbeleuchtung, 1883, p. 717. PHOTOMETRIC STANDARDS. 127 objective is at the same distance from the candle as from the divided scale ; next, by means of the screws a and 6, the image of the candle is regulated until it is clearly visible on the glass scale. At this instant the image of the flame is equal to the original in size, and its height is read directly on the scale. Precise measurements of the height of the flame of the candle pre- sent some difficulty on account of its irregularity. The lower edge of the flame cannot always be seen; this edge, of bluish color, is frequently hidden by the edges of the paraffine or stearine cup which is formed about the wick. Further, it is rarely of the same height on different sides. Finally, the top of the flame generally has three points, especially when the height is considerable ; the middle point is larger and longer than the lateral points ; but very fre- quently one of these flares, especially when the flame is about 50 mm. high. Measurements are then impossible. Measurement of the Consumption of Candles. 85. In general, for normal candles, a definite hourly consumption is prescribed ; the height of the flame plays a still more important rdle ; in fact, unless the candle burns freely and uniformly, a fixed consumption of material is out of the question. Now in all photometric observations it is necessary to snuff the candle ; at every operation of this kind its consumption is changed, so that the height of the flame, whose variations may be followed, should be the characteristic element of the luminous intensity of the candle, and not its consumption, which is modified at each snuffing of the wick. Below are some figures given by Kruss concerning the consump- tion of various candles first burning freely, then snuffed at regular intervals. Candle. Burning freely. Snuffed. Stearin6 . ... 10.20 grams. 8.78 grams. ParaffiiiG . . . 7.34 " 7.61 " Sp6rmac6ti 7.265 " . 7.45 " The consumption of material may be measured by means of Deleuil's apparatus employed for the carcel lamp. We give, besides 128 PHOTOMETRY. (Fig. 42), the description of a particular balance* constructed by Kruss and specially adapted to determining the consumption of candles. The arms of the balance are in the ratio of 1 to 2; the two candles which generally serve as a double standard, in order to diminish the variations of luminous intensity, are placed at the end of the shorter, so as to diminish proportionally the vertical displacement of the flame during the comparison. The double candlestick A may move vertically within wide limits. The box <7 encloses a Leclanche cell, one of whose terminals is connected FIG. 42. Candle Balance. through the electro-magnet of the bell G to the index Z\ the other terminal is connected to a small pin H, which, when it is in contact with the index Z, closes the circuit of the cell, and this rings the bell. The method of employment of this apparatus is the same as that of Deleuil's balance. Another apparatus to register the consumption of a candle has been employed frequently, by Monnier, among others. It is Elster's areometer, whose construction is well known. To make a measurement, when the candle has reached its normal condition, the pan is loaded until the areometer rests on the bottom Journal fur Gasbeleuchtung , 1885, p. 345. PHOTOMETRIC STANDARDS. 129 of the vessel ; the candle in burning becomes lighter, and the are- ometer rises ; when it passes the zero of the scale, the seconds- counter is started, and the areometer is allowed to rise, the position of the index being noted from minute to minute, which permits one to ascertain whether the consumption of the candle is regular. Fusion-Point of Stearine. 86. A knowledge of the height of the flame, combined with that of the hourly consumption of the candle, permits us to calculate the luminous intensity in terms of its normal value. These two points, the first especially, are of the greatest importance. A third should, however, not be neglected ; it is the degree of purity of the material of which the candle is made. In this regard the point of fusion and of solidification furnishes a valuable basis on which to measure the value of the material of the candle, for the presence of foreign bodies modifies this temperature considerably. Below are the values of the fusion-point of common candles, according to the measurements of Kriiss and Rudorff : the figures are the mean of a very large number of measurements. Candle. Kruss. Kudorff. Munich stearine 54.0 53.0 to 56.6 Gorman paraffine 53.7 49 to 54 English spermaceti .... 43.7 43.5 to 44.3 The method most used to obtain the fusion-point of greasy materials consists in enclosing the substance to be studied in a capillary tube, then heating it in a water-bath, measuring the temperature of the latter. The fusion-point is considered to be the temperature at which the substance becomes transparent or detaches itself from the tube and begins to move. This process is not exact. Another more exact method has been proposed by Loewe. An electric bell and a bath of mercury are placed in the circuit of a cell; a thermometer and two platinum wires are introduced into the mercury ; one of the wires, ending in a ball, is covered with a thin layer of the greasy substance, and the circuit is established as- soon as the fusion-point is attained. 130 PHOTOMETRY. Luminous Intensity of Standard Candles. 87. It is difficult to express numerically the relative luminous intensity of various candles, there being as many different values as observers. One of the principal causes of these differences should be sought in the lack of constancy in the luminous intensity of these photometric standards. We have already said that Schwendler found variations of 40 per cent in luminous intensity ; we must believe, however, that he took account neither of the height of the flame nor the consumption of the candle. At the other extreme is Kriiss, who claims to have been able to maintain the constancy of the light emitted by the candle within 3 per cent; this figure is evidently more favorable than can be obtained in industrial tests, where one can scarcely observe all the minute precautions used by this renowned German specialist. But let us mention the results of other observers. Dibdin, after extended investigation of luminous standards, in his report to the Metropolitan Board of Works of London, claims that candles give uniform results only by accident. Thus, in 454 measurements made with candles, 154, or 34 per cent only, gave results differing by less than 10 per cent from the mean. Heisch and Hartley, in an investigation of the same subject, found deviations of from 1.3 to 16 per cent from the mean, the mean deviation being about 7 per cent. On the other hand, Foucart found that, in his experiments, the intensity of the Star candle varies from 9.9 per cent above to 13.9 per cent below the mean, the total varia- tion being 23.8 per cent. An English commission, including Williamson, called attention, in its report to the Board of Trade, to the fact that candles taken in two different packages, or even in the same package, coming from the same factory, may give variations of from 14 to 15 per cent. We see then that it is scarcely possible under these conditions to give exact figures for the relative values of the different candles. So we shall limit ourselves to briefly indicating in the following table the relative values obtained by different observers. PHOTOMETRIC STANDARDS. HEIGHT OF FLAME OF 44.5 MM. 131 Candle. Kudorff. Buhe. Kruss. Monnier. Munich 100.0 100.0 100.0 100 German 107.9 106.4 106.0 87 5 English 108 7 108.7 104 5 78 4 HEIGHT OF NORMAL FLAME. Candle. Schilling. Kruss. Voit. Schiele. Munich 100 100.0 100 100 German 88 7 97 6 96 5 92 English 90.7 85.8 94.4 We give in conclusion the results obtained by Monnier relative to the value of the luminous intensity of ordinary candles, indicating the height of the flame and hourly consumption ; all the numbers are expressed in terms of the normal carcel lamp. Candle. Height of the Flame. Consumption (mean hourly). Value (mean in Carcels). English 46 mm 7.8 grams. 0.120 German 50 " 7.5 " 0.134 Munich 55.0 " 10.4 " . 0.153 Star 52 4 " 10.0 " 0.134 Petroleum Lamps. 88. The measurement of the intensity of very intense radiants can scarcely be made by direct comparison with the standard, candle or carcel lamp, because of the great difference in the intensities ; it is advantageous to employ an intermediate photometric standard whose constancy is sufficient throughout the duration of the tests, and which has a luminous intensity between that of the standard and that of the source studied. First among the light sources which realize the conditions re- quired of an intermediate photometric standard should be mentioned 132 PHOTOMETRY. petroleum lamps. Kound-wick petroleum lamps are nowadays uni- versally in use. The most simple form is that which is identical with the carcel lamp, a round wick with a double current of air and constricted glass chimney. We cannot give a detailed description of the principal types of petroleum lamps*, of which there is a great variety. We should bear in mind, however, that the majority of them have been brought out without taking sufficient account of the rational principles which are at the basis of the construction of lamps which should give a fixed and intense light with a minimum, consumption of petroleum. Among the round-wick lamps should be mentioned those which have a central disc designed to enlarge the flame and to promote combustion ; the chimney should not be constricted, to obtain a- maximum luminous output. The petroleum lamp has many advantages over the carcel lamp. First, it has no pump designed to raise the oil to the top of the wick ; petroleum being very fluid, it rises in the latter by capillarity with sufficient rapidity. It has been found, for instance, that a mineral oil having a density of 0.85 rises in the wick with sufficient rapidity to feed a normal flame, even when the height to be ascended reaches 200 mm. Further, the flame is quite at the top of the wick, so that the latter chars much more slowly ; it is not necessary to renew it for each measurement, and it is sufficient to clean it by wiping with a rag, without cutting it. It appears from precise measurements that the increase in the density of the petroleum, which is produced after the lamp has- burned for some time, has no sensible influence on the luminous intensity. The diminution of this depends principally on the con- ditions under which the lamp works. When first lighted, the petroleum is near the flame, and the wick is not yet charred ; the oil and the lamp are still cold. At the end of four or five hours the level of the oil has lowered considerably, but its tempera- ture and that of the lamp have increased, which is a compensation. If we represent graphically the variation of the luminous intensity with the time, we obtain, in general, a curve which rises in the beginning and then descends very slowly. See Dingler's Journal, Vol. CCLV. p. 39; Vol. CCLXIII. p. 374; VoL CCLXVII. p-. 145 and 265. PHOTOMETRIC STANDARDS. 133 At the International Congress of Electricians, in 1881, Wiede- mann extolled the petroleum lamp for photometric measurements ; in general, all who have used it as an intermediate standard have nothing but praise for it. Thus von Hefner-Alteneck warmly recommends the use of the petroleum lamp with a round burner or with the intensive burner ; the photometric measurements made in the Siemens and Halske laboratory have shown that this standard gives a uniformity quite sufficient for the majority of industrial measurements ; the quantity of petroleum used has very little influence on the variations of lumi- nous intensity ; the intrinsic intensity increases, however, with the fluidity of the liquid. Owing to government regulations as to mineral oils, the refined petroleum of commerce is of a sufficiently uniform quality. As, however, we compare at each measurement the intensity of the petroleum lamp with that of the photometric standard, the compo- sition of the petroleum has no influence except as regards the con- stancy of the light emitted. . Kriiss compared with one another two ordinary round-burner lamps of equal dimensions. In the space of one hour, the greatest variation in the luminous intensities of these lamps was 1.7 per cent, and the mean variation was 0.5 per cent. Liebenthal obtained less satisfactory results by comparing a petroleum lamp with the von Hefner-Alteneck acetate of amyl lamp ; the mean error of each observation was found to be about 3 per cent. It is possible, however, that the majority of these variations should be attributed to the variations of the Hefner standard. The remarks with respect to the influence of the height of the flame upon the luminous intensity of candles and of the carcel lamp are evidently applicable to petroleum lamps. However, the varia- tions in the height of the flame in the last are very slight. We should, in general, give to the flame the maximum height which it may have without flickering ; in this case, the variations in the height of the flame are the least sensible, and the lamp burns under the best conditions. It is, moreover, easy to guard against variations of luminous intensity produced by variations in the height of the flame. The petroleum lamp serves only as an intermediate standard, and its absolute luminous intensity has no importance from a practical point of view. For this reason, we may very advantageously employ 134 PHOTOMETRY. a species of screen of the Methven genus ( 96), which allows only the central part of the flame of the lamp to be seen. Variations in the height of the flame then exercise only an insensible influence on the luminous intensity of the standard. The most simple screen consists of a blackened metallic tube, with an opening of determined size, which is placed on the lamp coaxially with the ordinary glass chimney. The dimensions of the opening in the opaque tube are so chosen as to let pass only the rays of light emitted by the central part of the flame, little affected by variations of height. In closing, we give certain data on the luminous intensity of sev- eral petroleum lamps, data which we have selected from a work by Heim * upon common lighting apparatus, and from a research of Dolinin and Alibegowf, on lamps fed by Caucasian mineral oils (Nobel kerosene, density 0.822, at 15 C. ; Kagosin naphtha, density 0.858, at 15 C.). Heim. Diameter of Wick-holder in mm. Intensity in Normal Candles. Consumption of Oil per Hour per Candle. Ordinary round burner .... Victoria burner with central disc, 25 30 16.1 19.2 3.37 grams. 3.30 " It 14 It It 62 67.3 3.40 " Cosmos *' 30 22.9 3.70 " The above lamps consumed refined American petroleum (density 0.796, at 18 C.). Among the best central-disc burners should be mentioned the Mondbrenner of Schuster and Baer with a wick-holder of fourteen lines (1 line = 2.256 mm.); fed with kerosene, it gives a luminous intensity of 14.88 candles for an hourly consumption of 3.56 grams per candle. [Dolinin and Alibegow.] This burner has a central disc, and, at the base of the wick- holder, lateral channels planned for cooling the metal work. The greatest variation of intensity observed with this lamp was 1.32 candles (from 14.36 to 15.68 candles). * Lum. til., Vol. XXVI. p. 220. t Dingier 1 s Journal, Vol. CCLXVII. p. 265. PHOTOMETRIC STANDARDS. 135 THE HEFNER ACETATE OF AMYL LAMP. Benzine Lamps. 89. In the carcel lamp, as in candles, the wick is one of the principal causes of irregularities of the flame. It should then be suppressed. But to obtain a standard flame without a wick, or one in which its influence is reduced to a minimum, recourse should be had to easily combustible liquids, which become volatilized by the heat of the flame and burn in the form of vapor, unlike rape-seed oil, petroleum, etc., which require the direct action of the flame on a wick saturated by the liquid. Benzine or ligroin lamps have been employed as secondary photometric standards. Thus in 1877 Eitner* declared himself pleased with the us3 of a small lamp fed with benzine which gave satisfactory results ; the round and compact wick is placed in a very thin tube of brass and extends about 10 mm. beyond it; the latter is moved by means of a rack and pinion in a second tube which serves to limit the flame ; the wick, 7.5 mm. in diameter, is brought to the level of the outer tube, and the combustion of the benzine is effected without charring the wick too much. A platinum sight serves to regulate the height of the flame. The luminous intensity of this lamp is in the neighborhood of one candle. Ordi- nary benzine lamps may render excellent service in certain photo- metric studies. There are to be found, for instance, in the market, small benzine or spirit lamps which give good results as photometric standards, ; s Uppenborn | has shown. By means of a grooved sheet of metal, the glass is so placed that the upper edge has a constant determined height above the wick-holder (e.g. 45 mm.). The edge of the glass then serves to sight the top of the flame, and its height is maintained constant by means of the rack and pinion. When the height of the flame is kept constant, these small lamps furnish light of remarkable constancy; it is sufficient to compare them from time to time with one of the usual standards. Eitner's lamp, as well as all those which are based on the combus- tion of mineral oils, is affected by the same cause of error. These * Centralblatt fur Electr., 1885, p. 711. t Lum. EL, Vol. XXVIII. p. 532. 136 PHOTOMETRY. liquids are not of well-determined chemical composition, but are mixtures of different substances having different boiling-points and variable compositions ; they cannot be obtained in conditions which are always identical. They have further the disadvantage of not burning uniformly, the combustion at first being at the expense of the most volatile materials ; there remains finally a product volatil- izable with difficulty, which requires other conditions of combustion to furnish the same flame. These considerations and a great number of tests of different liquids induced von Hefner- Alteneck * to take as a combustible acetate of amyl. This liquid is fluid and possesses a very intense, agreeable odor. It may be easily obtained pure by distilling crys- tallizible acetic acid, or an acetate, with sulphuric acid and amylic alcohol. It is manufactured in great quantities for perfumery ; its boiling-point is very constant at 138 C., and its price is not high. The Hefner Lamp. 90. The von Hefner- Alteneck lamp is a simple spirit lamp (Figs. 43 and 43 bis) ; the inventor retained the wick because the lamp is manipulated more easily, and because, further, the wick does not char in burning acetate of amyl; its object is, in fact, simply to suck up the liquid which is disengaged as vapor when the tempera- ture reaches 138 C. The wick-holder is a German silver tube, 8 mm. in interior diam- eter, 0.15 mm. thick, and 25 mm. high. The normal intensity of the lamp is determined by the height of the flame ; this height is normally 40 mm., or five times the diam- eter, measured from the top of the wick-holder ; it is regulated by raising the wick more or less in the latter. The normal height is kept by means of a sight fitted to the lamp. The flame should burn freely in the air, without a glass chimney; however, a straight glass tube is sometimes used, 88 mm. in height, and 55 mm. in diameter ; under these conditions the luminous intensity of the 40 mm. flame diminishes 2 per cent. The wick should be made with great care ; it should exactly fill the German silver tube without being crowded. One may make it himself by placing parallel to one another ordinary cotton threads, until the required diameter is reached. It is not advantageous to * Lum. l., Vol. X. p. 601 ; Electr. Zeitsch., Vol. IV., 1883 ; Vol. III. p. 20, 1884. PHOTOMETRIC STANDARDS. 137 employ, as has been proposed, a wick whose end is made of threads of amiantus [a fine kind of asbestos] ; the complication which results is not compensated by the slightly greater uniformity of the light FIG. 48. Hefner Lamp. thus obtained ; and, further, it is not proved that the intensity of the latter is unaltered ; moreover, the amiantus does not at all dis- pense with cutting the wick from time to time. The normal height of flame of 40 mm. was adopted because the 138 PHOTOMETRY. lamp then gives a light equal to that of an English candle whose flame is 43 mm. in height. However, Bunte * found that the von Hefner- Alteneck unit corresponds to the English candle with a flame 45 mm. in height, and Liebenthal concluded, from more than 200 compari- sons, that the flame of the acetate of ainyl lamp, 37 mm. in height, has the same luminous intensity as that of the English candle 43.2 mm. in height. These differences are not exaggerated if we S FIG. 43 bis. Hefner Lamp. take account of the want of uniformity of these two light standards, and the difficulties of measuring with exactness the height of the flame. Some comparisons, made with the greatest care with perfected apparatus, have been effected by the commission on photometric standards of the German Society of Gas Engineers, and by Lummer and Brodhun, of the Physico-Technical Institute of Berlin. * Journal fur Gasbeleuchtuny, 1885, p. 796. PHOTOMETEIC STANDARDS. 139 Below are the results obtained, which are the mean of a great number of measurements made with different lamps and candles. 1 German candle equals/ L223 Hefner units ( German Commission). 11.162 " " (Lummer). 1 English candle equals 1.129 " " (German Commission). The difference of 6 per cent between the results of the commis- sion and those of Lummer and Brodhun shows well the difficulties of obtaining photometric standards with free combustion. The intensity of the Hefner standard is too small, especially now that the tendency is more and more toward employing intense radi- ants ; the color of the flame is somewhat red, on account of its rela- tively low temperature. It is the richest in red rays of all light standards. On this account, also, we cannot use it with advantage in the photometry of incandescent and arc lamps. Variations of the Hefner Standard. 91. The sole advantage of the acetate of amyl lamp is to be found in its great constancy ; on this point all those who have used it agree. Thus, Liebenthal determined from a great number of measurements that the mean error of one observation varies between 0.5 and 1.5 per cent. In 225 observations by Dibdin with the Hef- ner lamp, the result differed from the mean by a quantity less than 1 per cent in 206 (90 per cent of the measurements). The causes which influence the value of the acetate of amyl standard proceed principally from the state of the surrounding air. The vitiated air of a room has a sensible influence on the illuminat- ing power of the lamp , this is easily noticed by comparison with an incandescent lamp. The influence of the variations of the baro- metric pressure in a given place has not been determined ; it ought, however, to be sensible on carrying the lamp to elevated places ; besides, this influence is sensible in all standards based on com- bustion. The temperature of the place of observation has no influence on the intrinsic value of the light standard; we notice only that the variations of the flame are a little greater when the temperature is slightly lower. According to the directions of von Hefner-Alteneck, measure- ments may be commenced ten minutes after lighting ; but this space 1 40 PH O TOMETR Y. of time is somewhat short, and it is better to wait at least forty-five minutes *. The illuminating power of the acetate of amyl lamp varies greatly with the height of the flame, which is slender, very unsteady, and whose height it is difficult to measure. In this is found one of the great inconveniences of the Hefner standard. It is neces- sary for photometric measurements that a special observer should indicate the moment when the normal height of the flame is attained. The most exact process of measurement is based on the employ- ment of the cathetometer, but we can only take time for this solu- tion in the scientific researches of the laboratory. Under these conditions the height of the flame may be measured with a mean deviation of 0.2 mm. Much attention is necessary, however, to arrive at this result, because of the influence of the edge of the flame. The height of the flame as measured by means of the sight fitted to the lamp has a mean deviation of 0.5 mm. ; deviations of 1 mm. are, however, possible. We may easily adapt to the Hefner lamp an apparatus for measuring the height of the flame analogous to that which we described in speaking of candles f. The lamp has a screen at the side which supports at its upper part a tube closed at one end by an achromatic lens ; a second tube which moves on the first carries a sheet of ground glass on which a millimeter scale is engraved ; its fortieth division corresponds with the center of the lens, and is 40 mm. above the end of the wick- holder : the image of the flame is projected on this glass, and its variations are followed without difficulty. This permits the meas- urement of the height of the flame with a mean deviation of 0.3 mm., which corresponds to a deviation of 0.8 per cent in the luminous intensity. This mean deviation of from 0.2 to 0.3 mm. has to do with the measurements of one and the same observer. The results of two observers are less concordant t, and differ very frequently by from 0.5 to 0.6 mm. Liebenthal found that the luminous intensity of the acetate of * Journal fur Gasbeleuchtung, 1890, p. 33. t Zeitschrift fur Instrumentenkunde, 1890, p. 133. J Zeitschrift fur Instrumentenkunde, 1890, p. 131. Lum. El., Vol. XXVII. p. 413, and Vol. XXXI. p. 113. PHOTOMETRIC STANDARDS. 141 amyl lamp is expressed for a height of flame of less than 40 mm. by the formula 1=1-0.038 (40 -7i). For heights greater than 50 mm. the formula becomes 7=1 + 0.025 (ft -40). Below 40 mm. the intensity increases more rapidly than the height ; above, on the other hand, the increase is sensibly propor- tional. The dimensions of the wick-holder indicated by Von Hefner- Alteneck correspond to the maximum luminous intensity, for Lieben- thal found a diminution of about 1 per cent on increasing or dimin- ishing by 2 mm. the diameter of the German silver tube. As to the free height of this tube, a difference of 1 mm. produces a varia- tion of only 0.2 per cent. Notwithstanding these favorable results, it is certain that dif- ference of make produces considerable difference in the luminous intensity of the Hefner standard. Thus six standard lamps com- pared by a special commission of the German Society of Gas Engi- neers with the best lamp belonging to the Physico-Technical Institute at Berlin produced luminous intensities expressed by the following figures: 0.987, 0.993, 0.993, 0.965, 1.016, 0.981. These numbers represent differences of from -f- 1.6 per cent to 3.5 per cent. The same commission found also a difference of 2.9 per cent between the illuminating powers of two lamps, one constructed by Siemens, the other by Kruss at Hamburg. Finally lamps of Siemens, Kruss, and the Physico-Technical Institute of Berlin gave differences included between -f- 8.9 per cent and 3.2 per cent. Under these conditions, it is difficult to adopt the Hefner lamp as an absolute standard when one of the principal advantages claimed in its favor, the facility of identical reproduction, does not exist. Influence of the Purity of the Acetate of Amyl. 92. The influence of impurities in the acetate of amyl on the luminous intensity of the Hefner standard has been investigated with great pains by Liebenthal. It is known that acetate of amyl, C 7 H 14 2 , whose boiling-point is between 138 and 140 C., is obtained by the action of sulphuric acid on amylic alcohol, C 5 H 2 (boiling-point 129 to 133 C.), and 142 PHOTOMETli Y. vinegar (boiling-point 117 to 119 C.). This ether very frequently contains variable quantities of amylic alcohol, acetic acid, and water. It may be purified by a fractional distillation, but this long opera- tion should be made with great care, because of the slight difference between the boiling-points of the impurities. If these impurities are considerable, four parts of the liquid should be mixed with one part of a concentrated solution of com- mon salt plus a small quantity of calcined magnesia; shake well and repeat this operation several times ; next separate the common salt solution, and shake the liquid again with pulverized chloride of calcium ; it only remains to rectify the acetate of amyl at a tempera- ture of about 80 C. Liebenthal found that impurities diminish the illuminating power; for amylic alcohol, however, the diminution is so slight that it may be neglected in practice ; the presence of 20 per cent of amylic alcohol lessens the illuminating power by 1.1 per cent only. Acetate of amyl saturated with water gives also an illuminat- ing power practically equal to the normal value ; the diminution is 0.5 per cent. A diminution of 3 per cent in the illuminating power has been found with a sample of acetate of amyl containing 10 per cent of alcohol and 5 per cent of water, but this change is not found in practice. It follows then from these measurements that the composition of acetate of amyl does not cause the illuminating power of the Hefner lamp to vary for a height of 40 mm., except within very narrow limits. The influence of impurities is more considerable on the stability of the flame. In proportion as the impurities of the liquid increase, the flame becomes less and less quiet, and is affected with very slight oscillations, which may, however, in certain cases, be percepti- ble to the naked eye. The instability of the flame may be explained by assuming that the impure liquid, unalterable in a closed vessel, is altered little by little, in proportion to its combustion ; it is fur- ther noticed by the production of verdigris and the charring of the wick ; the latter then cannot draw up the liquid regularly. The composition of the liquid should be tested with care before proceeding to measurements, and in case of doubt, it should be submitted to special distillation. Below is the method indicated by Bannow* for verifying the purity of acetate of amyl. * Elrctrotech. Zeitschr., 1891, pp. 122, 177, 193. PHOTOMETRIC STANDARDS. 143 1. The density of the liquid should be between 0.872 and 0.87C at 15 C. (test for alcohol). 2. The mixture of equal volumes of acetate of amyl and benzine (or sulphuret of carbon) should remain clear and liquid (test for amylic alcohol or ethyl hydrate ; the water separates in globules under the action of the sulphuret of carbon) . 3. On shaking in a graduate 1 cc. of acetate of amyl with 10 cc. of 90 per cent alcohol and 10 cc. of water, a clear and liquid solu- tion should be obtained (test for toluene, etc., not determined by the second test). 4. A drop of acetate of amyl should leave no greasy trace on a sheet of white paper after evaporation (test for oils, tar, and other greasy materials). The Hefner standard has been adopted in Germany by the Society of Gas Engineers, and official sanction will soon be given it by the Physico-Technical Institute of Berlin. It may be asked, in conse- quence of the numerous sources of error in this light standard, if the advance brought about by replacing the candle by the Hefner lamp is sufficiently great to justify the introduction of this new absolute standard. (See Appendix C.) The Giroud Standard. 93. In 1882, Giroud proposed a new photometric standard designed primarily for the testing of gas, but which, in certain cases, may be used with advantage in electric photometry. This standard is based on the combustion of gas in a determined burner, under a constant and well-defined pressure. Audouin and Berard* investigated carefully the circumstances which have an influence 011 the light emitted by a gas-burner, among which should be mentioned, in addition to the composition and pres- sure of the gas, the dimensions, form, and nature of the burner employed. The Giroud standard f consists of two lights, one of which serves to determine the constancy of the other, while permitting measure- ments of its variations. These two lights are fed by ordinary illuminating gas, which is procured with as much facility as oil, stearine, etc., if not more. One of the two burners of the standard is a candle-burner with a single opening of 1 mm. ; the other is an * Ann. de Chim. et de Phys., 3 e serie, Vol. LXV. t Journal des usines a gaz, 1881 and 1882. 1 44 PH O TOMETE Y. Argand burner. The lights produced are in the ratio of 1 to 10, and since they result from the same gas, they remain in the same ratio, regardless of accidental variations entering into the quality of the latter. Every change in the real intensity is manifested in the standard by a change in the surface of the flame or in its dimensions. It is impossible to determine this change in dimensions in the Argand burner, while it is easy to recognize and measure it with the single- aparture burner, in which the slightest change is shown in a very sensible manner in the length of the flame. It amounts then to a single measurement of this length ; if it remains constant, it follows that the intensity of the candle-burner and consequently that of the Argand burner, are not modified ; if the former varies, the extent of this variation measures the change undergone by the Argand burner whatever be the number of units the burner represents. Giroud's Candle-burner (bee-bougie) Standard. 94. Giroud has given to the candle-burner the value of y 1 ^ carcel, that is, the value which is assumed approximately for the candle, and to the Argand burner the value of one carcel. Invariability of the length of the flame is necessary during the measurements. The consumption of gas should then be constant, which necessitates the employment of a special meterage, effected by the rheometer of Giroud. The rheometer is an instrument for continuous meterage, appli- cable to the flow of both liquids and gases. Figure 44 represents it in working size for ordinary gas-burners. The current indicated by the arrows raises a movable barrage whose vertical movement should be quite free ; it is formed for this purpose by a cap gliding without friction in a- bath of glycerine which serves to lute it. This cap is pierced by an orifice which has nothing in common with that of the burner, and at this ori- fice there is established a velocity which has nothing in common with that of the current. It follows that we may place on the rheometer FIO. 44. Giroud Rheome- any burner, or even none at all, without affecting the flow through the rheometer. Below is the description of the candle standard of Giroud, of which Fig. 45 gives a vertical section. PHOTOMETRIC STANDARDS. 145 It is in fact only a rheometer whose valve is under instead of above the cap C. The conical cover of the valve is soldered at its base to the tube A which plunges in the glycerine bath of the chamber E. The inner section of this tube is exactly equal to that of the opening forming the seat of the conical valve ; the rod which connects the cone to the cap is a small open tube. In this way the movable part, consisting of the cap, the cone, and the tube B, rests sus- pended in equilibrium in the current and cannot move except in a vertical direction, under the pressure of the gas ; it is shown that this resisting pressure is constant, for it is ex- pressed by the formula, 8-8 P being the pressure of the gas, P' the counter-pressure produced by the burner, p the weight of the mov- able part complete, S the surface of the cap C, s the inner section of the tube A. When the pressure P P' in- creases, the cap C lifts, and the coni- cal cover of the tube A partly closes the opening, through which a smaller quantity of gas then passes; equi- librium is re-established when the FIG. 45. Giroud Candle-burner (bee- bougie) Standard. normal pressure PP' has been attained anew. The consumption only depends then on the diameter of the opening of the cap C and on the nature of the gas. The sight shown in the cut is only a crude representation; the measurement is made from the burner to the extreme top of the flame, the place where the red point which terminates it ceases to be visible. The rheometric opening in the cap is of such a diameter that it is always necessary to make use of the cock .fiTto obtain the volume which will give the normal height of the flame with the ordinary flow of gas. 146 PHOTOMETRY. The burner is of soapstone, giving the freest access to the air at the point where the flame begins. The opening of this burner should be 1 mm. ; this may be determined by a gauge. Giroud adopted a height of flame of 67.5 mm., for which the candle-burner gives a luminous intensity of exactly y 1 ^ carcel. There is between the height and the intensity of the flame of the gas-burner of single opening a ratio which remains constant for heights between 45 and 120 mm. It is the same as in the carcel lamp, where there is between the weight of the oil consumed and the luminous intensity a ratio which remains constant for consump- tions comprised between 40 and 44 grams of oil per hour. Below are some figures in regard to this : Height of the Flame of the Candle-burner (bee- bougie) in Millimeters. Intensity in Carcels. Height of the Flame of the Candle-burner (bee- bougie) in Millimeters. Intensity in Carcels. 45 0.0505 75 0.1165 50 0.0614 80 0.1275 60 0.0835 90 0.1495 65 0.0945 100 0.1715 67.5 0.1000 110 0.1935 70 0.1055 120 0.2155 The variation in luminous intensity is then 0.0022 per mm. of variation in the height of the flame. The opening should be exactly 1 mm. in diameter ; a variation of 0.05 mm. produces a variation in luminous intensity of 3 per cent with the same quantity of gas; it is very easy to determine this diameter within 0.01 mm., so that we may be sure of the lumi- nous intensity within 1 per cent. The influence of the composition of the gas on the intensity of the candle-burner has been found negligible, care being taken to maintain the flame at the normal height of 67.5 mm., by a suitable regulation of the rheometer ; with an inferior quality there simply results a more considerable consumption of gas. The same remark applies to variations in the density of the gas ; the consumption alone varies with this latter. For a density of 0.4, that of air, the consumption of the candle-burner is 25 liters per hour. As to the influence of the atmospheric pressure, Giroud has shown that it is negligible ; it is the same with variations of tem- perature between 15 and 25 C. PHOTOMETRIC STANDARDS. 147 The flame of the candle-burner is then an absolute standard whose intensity has been so made by definition as to equal J^ carcel, but which is always susceptible of being exactly reproduced. Relative Photometric Standards of Giroud. 95. However, the advantages of the Giroud standard are great- est in the comparison of intense radiants, for which we then use the relative standards whose brief description follows. It is an observed fact that in Paris, for instance, when the flame of the absolute standard has been brought to 67.5 mm. by means of the cock A", the rheometric consumption is 25 liters per hour of standard gas at a density of 0.4. We may easily reproduce this rate of flow with an apparatus provided with a cock AT, if we make in the cap a rheometric opening of suitable dimensions, with which we need not concern ourselves further. The two photorheometers B and C, in Figs. 46 and 47, are fitted with burners suitably chosen, and regulated so as to give that vol- ume of gas, whatever it be, which is necessary in order that the burners may give, one 10 times, the other 50 times, as much light as A gives, when the same gas supplies them all. If the gas is standard, A should be -fa carcel, B 1 carcel, and C 5 carcels; if the gas is not standard, the flame A should be shorter or longer than 67.5 mm., and each millimeter difference will represent a change of 2.2 per cent in the value of the standards B and C. To measure the flame of the candle-burner exactly, a sight of which Fig. 47 gives a sufficient idea, is used ; the line of sight is determined by the lower edge of the screen a, and by the point of tangency of the two circular holes in the screen b. It does not appear, however, that this method of measuring the height of the flame is sufficiently exact. At least this is the conclusion from numerous measurements made by Heisch and Hartley under the authority of the Gas Institute. The measurements of Heisch and Hartley* showed that the Argand-Giroud burner of \ carcel for a length of flame of the candle- burner of 67.5 mm., equalled 10 English candles when the flame of the candle-burner was 69.5 mm., the gas employed having an illu- minating power of 15.8 candles. * Journal des usines a gaz, 1884 and 1885. 148 PHOTOMETRY. FIGS. 46 and 47. Giroud Photorheometer. Here are some results among others, which show the agreement realized between the direct measurements of the luminous intensity of the Argand-G-iroud burner and the intensity calculated according to the instructions of the inventor. Illuminating Power of the Gas*. Height of the Flame of the Candle-burner. Luminous Intensity (real) of the Argand Flaine. Luminous Intensity (calcu- lated) 'of the Argand Flame. Difference fn per cent. Candles. 15.47 69.0 10.31 9.89 + 4.2 15.80 69.5 10.00 10.00 0.0 15.80 69.5 10.13 10.00 -f-1.3 15.64 69.5 10.17 10.00 + 1.7 15.94 68.5 10.31 9.78 + 5.4 15.90 69.7 10.23 9.90 + 2.7 16.06 71.6 10.80 10.46 + 3.2 15.98 72.0 10.85 10.55 + 2.9 * Let us recall briefly what is meant by illuminating power (titre} of gas. In France the illuminating power of gas is fixed by stipulating the consumption PH O TOMETRW S TAN DA RD& . 149 The mean deviation is 2.5 per cent. The conclusion of Heisch and Hartley is favorable to the Giroud standard. These two engineers think in fact that, in ordinary practice, with a better arranged sight, the errors of the instrument should not exceed 3 per cent, the illuminating power of the gas varying between 15 and 16.5 candles. Uppenborn also made some measurements* of the luminous intensity of the Giroud candle-burner of one opening, which tend to prove that the rheometer does not regulate the flow of gas, and consequently the height of the flame, so exactly as is generally supposed. Uppenborn found that the luminous intensity of the candle-burner increases slowly after lighting for a period often extending over two hours. His values for the Giroud candle- burner in terms of the Hefner standard, for different heights of the flame, are Height of Flame in Milli- meters. Luminous Intensity in Hefner Units. Variations of the Luminous Intensity per Millimeter of Flame. 81 1.369 71 1.143 0.0226 61 0.965 0.0178 51 0.838 0.0127 THE METHVEN STANDARD SCREEN. 96. John Methveii announced in 1878, to the British Association of gas managers, that he had discovered that the portions of flames of gas of different qualities, burned so as to obtain perfect combus- tion in similar Argand burners, have equal illuminating powers. Methven further determined the particular parts of an Argand flame which emit the same quantity of light on supplying the burner with gas of different qualities so as to give a three-inch flame; he also found the means of avoiding the radiation toward necessary to obtain the luminous intensity of a carcel lamp burning 42 grains of purified rape-seed oil per hour. In England it is fixed by determining the num- ber of candles corresponding to a consumption of 5 cu. ft. (141.6 liters) of gas per hour. In the first case there is employed a Bengel burner of 30 openings, in the second, an Argand burner (Sugg's London Argand No. 1). * Lum. fil., Vol. XXVIII. p. 330. 150 PHOTOMETRY. the photometer of all rays other than those belonging to the con- stant portion of the flame. The original method of Methveii was as follows : in front of the burner, between it and the photometer, is placed a blackened copper screen. A rectangular opening, one inch high by a quarter of an inch wide, is made in the screen, which thus permits the passage of a quantity of light equal to that of two spermaceti candles only. The first tests were made using ordinary gas ; later Methven * undertook a series of measurements to determine the influence of the illuminating power of the gas on the intrinsic intensity cf the flame, and thus obtained, by an appropriate carburetting of the gas, an intrinsic intensity exactly com- parable with itself, and, besides, a tonst.mt luminous standard. He found that gases, originally of dif- ferent qualities, produce the same quality of light when they are carburetted and burned with the same burner in a flame 2.5 inches high. The hydrocarburet employed is a prod- uct of petroleum generally known by the name of gasoline. This has a very low spe- cific gravity and a very low boiling-point, and emits its vapors at the ordinary tem- perature, so that gas passing over its surface completely evaporates it at a temperature of 10 C. The carbureter employed by Methven is composed of many troughs of fine wire gauze, fixed on an inclined plane in a small rectangular chamber; the necessary quantity of hydrocarburet is determined and flows from a reservoir into the highest trough; the volatilization com- mences at once ; that which does not evaporate in the highest compartment falls into the second, and so on. The gas, on simply passing above the troughs in question, becomes saturated and is FIG. 48. Methven Screen. * Journal des usines a gaz, 1883. PHOTOMETRIC STANDARDS. 151 afterwards consumed by the burner. As the quantity of gasoline which flows into the carbureter is determined with care, it becomes completely volatilized, and thus a carburetted gas of uniform quality is obtained. Below is shown the effect of the carburetting produced by this apparatus on gas of different qualities. Illuminating Power of the Gas before Carburetting. Illuminating Power of the Gas after Carburetting. Variations. 10.51 candles. 62.86 candles. -f 0.54 candles. 13.82 60.38 - 1.94 " 16.25 61.92 - 0.40 18.85 62.49 -0.17 " 20.44 63.77 + 1.65 Mean . . 62.32 candles. The carbureter should be placed in a bath at about 10 C., in order to compensate for the cold produced by the evaporation of the oil. The Methven screen, in its most recent form, is composed of a movable plate carrying two silver screens ; one of them, having a rectangular opening 1 inch (25.4 mm.) long by 0.233 of an inch. (5.92 mm.) wide, is designed for use with ordinary non-carburetted gas; the other, which is used when gas, carburetted as indicated above, is burned, has an opening 0.585 of an inch (14.86 mm.) long by 0.310 of an inch (7.87 mm.) wide. The burner employed is Sugg's ordinary Argand burner with a glass chimney (Standard London Argand, No. 1). The base of the opening, when using ordinary gas, is 1 inch (25.4 mm.), and when using carburetted gas, 0.96 of an inch (24.38 mm.) above the top of the burner ; the horizontal distance from the center of the flame to the screen is 1.5 inches (38.10 mm.). The height of the flame from the burner is 3 inches (76.2 mm.) for carburetted gas; these two heights of the flame are defined by a double set of horizontal wires forming sights fixed on the screen. The chimney of the Argand burner is 2 inches (50.8 mm.) in diameter and 6 inches (152.4 mm.) in length. The Methven standard, being very simple in construction, is not subject to derangement, and its use is extremely easy. When employing ordinary gas, it is much better than the candle in an open-air photometer. The indications of the Methven screen with 152 PHOTOMETRY. carburetted gas are very concordant. Thus Dibdin, in a very exten- sive investigation of the different light standards, found, out of 283 experiments, 211 or 74 per cent, in which the results did not differ by 1 per cent from the mean. The Giroud burners and the Methven screen may render marked service as intermediate standards, always on the condition of having their values determined in comparison with the absolute standard. By supplying these burners with gas stored in the gas-holder of the laboratory at the commencement of the experiment, we have at our disposal a source of light which remains constant for many hours, and whose employment requires no delicate manipulation. This is of considerable advantage, and makes these burners, notably that of Giroud, valuable auxiliaries in photometric researches. Vernon-Harcourt's Pentane Standard*. 97. The objections which may be made to photometric standards in which ordinary illuminating gas is employed, evidently cease if we are able to have gas of constant composition. It is this constancy of composition which Methven sought to realize, in a certain meas- ure, by replacing ordinary gas by carburetted gas. A more perfect solution of the problem has been found, after numerous trials, by Vernon-Harcourt ; the combustible employed by him is air carburetted by means of volatile carburets of hydro- gen, products of petroleum. The carburet is prepared by a frac- tional distillation of gasoline, previously washed with sulphuric acid and caustic soda. The liquid decanted is distilled four times, successively at 60, 55, 50, and lastly at 50 again. The prod- uct obtained is composed of hydrocarburets of the paraffine series, C n H 2n + 2 , principally pentane, C 5 H 12 , mixed with its homologues, tetrane, C 4 H 10 , and hexane, C 6 H 14 . Its specific gravity at 15 C. varies between the limits 0.628 and 0.631. We may employ air carburetted with pentane in two ways : in one of the standards the gas is prepared in advance and stored in a special gas-holder ; in the other, it is prepared in proportion and at the same rate as it is burned, which is precisely what takes place in the case of a lamp or candle. The following is the way, according to Monnier t, of preparing stan- dard carburetted air after the directions given by Vernon-Harcourt. * Elect. Review (London), May 6, 1887. t Journal des usines a gaz, 1883. PHOTOMETRIC STANDARDS. 153 To prepare the standard carburetted air, the hydrocarburet is left to mix with the air by the diffusion of its vapor in the proportion of 3 cu. in. of liquid to 1 cu. ft. of air measured at a pressure of 76 cm. of mercury, and at a temperature of 15 C. ; the proportion of pen- tane, when in a state of vapor, is 7 volumes of pentane mixed with 20 volume of air. The gas-holder (Figs. 49 and 50) is composed of a cylindrical receiver 7 cu. ft. in capacity, suspended and balanced in an annular cistern filled with water. A graduated scale, fixed to the receiver, serves to measure the volume of the gas. In the cap, which is plane FIGS. 49 and 50. to avoid waste space, are found two tubes : one gives access to a ther- mometer ; in the other is fixed a glass receiver of special form. To prepare the mixture, we blow into the receiver 3 cu. ft. of air measured at 76 cm. pressure of mercury and at 15 C. ; a graduated pipette which contains 9 cu. in. is filled with pentane. The point of the pipette being introduced into the lateral tube L of the vessel V (partly full of water), the cock is opened; the pentane flows in and rises to the upper part of V and enters the receiver by the tube T. The last part of the pentane is driven in by blowing gently. When all the liquid has entered, the pipette is withdrawn, and the last part of the pentane is forced into the receiver by pouring some water into the lateral tube L. The diffusion is complete in five 154 PHOTOMETRY. or six hours ; at this time, the volume of gas should be 4.05 cu. ft., with an allowable variation of 1 per cent. The vapor of the hydrocarburet employed to carburet the air should be very slightly soluble in water, so that the composition of the gas does not become altered by contact with the water in the gas- holder : this condition excludes the employment of defiant gas, ether, or benzine, which are quite soluble in water, while pentane is very slightly so, 100 volumes of boiled water dissolving only 0.92 of a volume of pentane vapor. This solubility is sufficient to slightly modify the composition of the first gas prepared in a receiver over pure water ; but, after an operation or two, the water is saturated ; and as variations in the com- position of the gas may only come from a temperature change in the coefficient of solubility, they are very slight. The vapor of pentane behaves like a perfect gas within the ordi- nary limits of temperature and pressure. The mixture of air and pentane vapor constitutes then a gas of constant composition. The burner adopted by Vernon-Harcourt is a candle-burner of yellow copper, because of the ease with which this metal is worked. The opening is circular; it is made in a copper plate 0.05 of an inch thick and should be 0.25 of an inch in diameter. This dimension may be reproduced within 0.001 of an inch ; that is, with an error of less than 0.8 per cent of the total section of the opening. The greatest diameter compatible with steadiness of the flame was chosen. The body of the burner is 4. inches long and 1 inch in diameter. The normal height of the flame is 2.5 inches measured from the opening of the burner; under these conditions, the normal con- sumption of gas is between 0.48 and 0.52 cu. ft. per hour. The height of the flame is shown by a platinum wire carried on a rod parallel to the burner. The gas is measured by means of a small meter, and its con- sumption is further regulated by a sensitive regulator. Under the above conditions, the Harcourt standard gives a- luminous intensity exactly equal to that of a spermaceti candle. For the needs of industrial photometry, we may obtain a quite intense standard of light, about ten candles, of great constancy, by using the pentane air gas of Harcourt in an Argand burner (Sugg's Standard London Argand, No. 1) combined with the Methven screen. It is this which has been done by Dibdin among others. It is even sufficient, in order to carburet the air in the Methven carbureter, simply to pass it over the liquid pentane. PHOTOMETRIC STANDARDS. 155 Dibdin found that under these conditions the height of the flame may vary between 2.5 and 6 inches without the quantity of light emitted upon the screen varying in a sensible manner. The normal height of the flame is then 3 inches, but a slight variation in this height hardly affects the standard. However, the pentane Argand does not afford any control over the working of the burner, so that we should hardly dream of employing it with safety in photometric measurements, still less of giving it a legal sanction. Laboratory Form of the Pentane Standard. 98. The air-gas lamp, in which the gaseous mixture is prepared at the time of combustion, has undergone some quite important modifications since the time when Vernon-Harcourt brought it out in its first form. This gave results which were little concordant, if we may judge from the numerous measurements of Heisch and Hartley, while the final form presented to the British Association in 1887, reproduced the light standard with very great exactness ; this is at least the conclusion from Dibdin's report, to which we shall return later. Following is the descriptio i of the laboratory form of the pen- tane standard, as made by Woodhouse and Eawson of London (Fig. 51). The admission of the gas to the burner is made exclusively under the action of gravity and without a regulator. The air and vapor are mixed in a reservoir M, whence they descend to the burner. At a certain point, the diameter of the tube through which the gas flows is reduced, and there is between this reduction and the height of the reservoir such a relation that, when the mixture, in the above indi- cated proportions, is introduced into the tube, it is burned with a flame 2.5 inches high. The pentane is introduced in the liquid state into the globe M y whence it flows into the reservoir B, where it is vaporized ; the vapor passes through C and H, and next descends by its own weight in the vertical tube which leads to the interior of the reservoir 72, where the mixture passes through the cock D and reaches the burner FG. To regulate the velocity and regularity of the flow of the mixture, the pentane vapors are passed through a thermometric tube which is stopped up for a greater or less distance by a platinum wire attached to a screw 0. We may thus give to the pentane the velocity of entrance necessary to make the flame exactly 2.5 inches high. 156 PHOTOMETRY. The level of the pentane in the reservoir has naturally a certain influence, of which account is taken in the following manner. The square box shown in the figure contains a rubber balloon filled with water and connected by a flexible tube to the reservoir ; when the level of the pentane is too low, the balloon is compressed by means FIG. 51. Pentane Lamp (Laboratory Model). of the screw ,7, and a certain quantity of water is made to enter the reservoir B below the pentane. In the opposite case this screw is loosened, and the water is allowed to descend again. The heavy copper disc Y suspended above the flame at a variable height serves to compensate for the influence of the external tern* perature ; the chimney G protects the flame from currents of air. PHOTOMETRIC STANDARDS. 157 Industrial Form of the Pentane Standard. 99. Vernon-Harcourt has simplified this apparatus still more, so as to make it portable and much less complicated without taking away any of its precision. Vernon-Harcourt's new lamp, instead of burning a mixture of air and pentaiie vapor, burns the vapor of pentane alone ; the flame is surrounded by a chimney which produces sufficient draught and steadiness ; it is as white as in the original form of the pentane standard, which is a very im- portant condition. The new standard lamp, repre- sented in Fig. 52, has a form analogous to that of ordinary alcohol burners, with a metal chimney in addition. The metal- lic chimney producing a strong current of air gives the necessary steadiness to the flame and in- creases its temperature, which also gives it a whiter color. Use is made of a wick, which would be a serious disadvantage if combustion took place at its end ; this is not the case, for it simply serves to raise the pentane by capillarity from the lower reservoir to the place in the wick- holder where it is vaporized under the influence of the heat produced by the combustion of the vapor, 5 or 8 cm. higher. The wick enters with slight friction in a tube open at both ends and itself surrounded by a metallic covering much larger, intended to keep the temperature more constant. The combustion of the pentane vapor takes place at the end of this outer tube ; the whole is surrounded by a third tube much larger, which FIG. 52. Pentane Lamp (Industrial Model). 158 PHOTOMETRY. contracts in its upper part so as to have only the diameter of the glass chimney. This chimney is enlarged at its upper end and is fixed to the metallic envelope of the lamp by means of the two movable arms shown in the figure. The working of the lamp is as follows : on raising the wick- holder and heating the inner tube a little, the pentane vapor is immediately disengaged and lighted. The outer covering with the chimney is then put on; the flame immediately rises, because of the increased draught, and its end enters the chimney. This has, at a height of 10 mm., two horizontal slits diametrically opposite, so that, by looking across, the height of the flame may be exactly regulated. Since the movable chimney is regulated in height, and the height of the flame is determined exactly by the two slits mentioned above, the portion of the flame included between the lower envelop and the chimney emits a perfectly definite quantity of light. We know that the quantity of light emitted by the central part of a flame is only very slightly affected by variations in the height of the later. Harcourt and the makers have carefully determined the dimensions of the lamp which correspond to a luminous intensity of one candle and two candles. By varying the height of the chimney, we may obtain any luminous intensity within the limits of the power of the apparatus. The height of the chimney is verified by means of a special cylindrical gauge of the same diameter as the lower part of the chimney, which is placed between the latter and the outer tube of the base ; the chimney is then fixed in this position by means of regu- lating screws. The variations in the height of the flame are very slight ; they become insensible ten or fifteen minutes after lighting. The base of the apparatus is made horizontal by means of a level, and a small mirror placed behind the slits facilitates observation of the height of the flame. The new pentane lamp is more easy of manipulation than the acetate of amyl lamp of Hefner- A Iteneck, since variations in the height of the flame have only a very slight influence on the lumi- nous intensity ; the flame is, further, much whiter. 100. There is a difference in the results obtained with Har- court's air gas, among the observers who have investigated this standard with care ; there is evidently a question of personal preference here. PHOTOMETRIC STANDARDS. 159 Thus while Heisch and Hartley favor rather the Methven screen, Dibdin, by reason of very extended and careful comparative measurements, considers that Harcourt's pentane lamp is, of all the industrial photometric standards, the one whose luminous intensity is the most constant and fixed. We quote the following from his report to the Metropolitan Board of Works of London : "The pentane flame fulfils all the conditions which may bo, imposed on it. Experiments showed that the preparation of car- bu retted air was easy and not dangerous, the measurement of the volume of air consumed simple and precise, the regulation of the height of the flame very exact, that this possessed all the constancy desirable when operated with care, and finally, that the color of the light was identical with that of a gas-flame. " Throughout the tests there was no noticeable defect in the stability of the light. The only precaution to be taken is to avoid currents of air." A variation of 2 per cent in the luminous intensity of the pen- tane flame is exceptional, while with candles, for instance, a vari- ation of 10 per cent is a common thing. As to the value of the pentane standard, Dibdin found that it was sensibly equal to an English candle. To sum up the investigation of different light standards based on combustion, we give here a table which recapitulates the numerous observations oi Dibdin. He includes in the first column the total number of experiments made on each standard, in the second the number of those whose results differ from the mean by less than 1 per cent, and finally in the third the ratio of these numbers. Keate's lamp* . . . . . . 244 98 *" 10 39 Pentane (original form) . Methven . . . . . . 468 . 282 373 211 80 74 Pentane-Argand . . * 243 212 87 Acetate of Amyl lamp Pentane lamp . . 225 154 206 150 90 97 * Keate's lamp is used in England alone ; we shall not dwell on its details, for it only differs from the carcel lamp in the oil used. It burns paraffine oil in place of rape-seed oil ; but its conditions of working are analogous to those of the carcel lamp, and all that we have said concerning the latter is applicable to this. 160 PHOTOMETRY. These results represent to some extent the respective values of the different photometric standards ; but before being accepted as final, this classification should be confirmed, for exactness of photo- metric measurements depends greatly on conditions peculiar to the observer. STANDARDS BASED ON THE INCANDESCENCE OF CARBON AND OF PLATINUM. Schweudler Standard. 101. The Schwendler standard is composed of a platinum strip in the form of a horseshoe ; this strip being cut from a sheet of large dimensions, there are kept two ends of considerable surface connected to the terminals of the apparatus ; the heating of the conductor thus takes place solely in the horseshoe part. The light unit adopted by Schwendler (P.L.S.) is the quantity of light emitted by a platinum strip of ths preceding form, 2 mm. in width, 36.28 mm. in length, 0.017 mm. in thickness, weighing 0.0264 mg., traversed by a constant current of 6.15 amperes. The causes which influence the quantity of light emitted by a platinum strip heated by the electric current are too numerous for one to count on the constancy of the light emitted, if one is limited to controlling simply the constancy of the current. The variations in the emissive power, as well as the diminution of the section of the platinum strip under the influence of a prolonged incandescence, are factors of which it is difficult to take account. These circum- stances have, from the beginning, inspired a certain distrust of the Schwendler standard, so that its use has not spread either in indus- trial measurements or in scientific researches. The Incandescent Lamp as an Absolute Standard. 102. Preece, considering that incandescent lamps of a given type, coming from the same maker, present only insignificant differ- ences among themselves with respect to luminous intensity and efficiency, thought that there might be obtained, by means of the incandescent lamp, a very convenient photometric standard suffi- ciently exact for the majority of industrial measurements. It would then be sufficient, as in the Schwendler standard, to maintain the current at a determined intensity. PHOTOMETRIC STANDARDS. 161 This idea was advanced anew by Edison, some time after Preece's communication ; the variations in the emissive power of the carbon filaments, sometimes very sensible from one lamp to another, and the greater or less transparency of the bulb, are so many factors opposed to the adoption of a unit of this kind. We do not wish to say by this that one ought, a priori, to avoid the use of incandescent lamps in photometric measurements. In certain cases it is, on the contrary, very advantageous to use one of these lamps as a secondary standard. But the adoption of a typical incandescent lamp as an absolute standard will not take place very soon ; for its inconveniences are not of such a nature as to be over- come without considerable improvement in its construction. How- ever, if the invariability of the luminous intensity of an incandescent lamp for a constant expenditure of energy can ever be attained, the incandescent lamp will furnish a very convenient absolute photo- metric standard ; it might then be defined by the nature and dimen- sions of the filament and the energy absorbed, expressed for instance in ergs per second. The Incandescent Lamp as a Secondary Standard. 103. Until within the last few years, industrial photometric measurements were principally made to verify the luminous intensity of gas-lights. It is in this that we may find the ^explanation of the great number of photometric standards based on the combustion of ordinary gas or a special gas in a typical burner. These standards are very convenient in the photometric laboratories of gas manufac- tories, where one has at his disposal all the accessory apparatus indispensable to their successful operation. It is not so in industrial electrical laboratories where one has at his disposal generally a simple connection with a gas supply. But these laboratories possess, on the contrary, a complete outfit for the production and regulation of light by means of incandescent lamps. It is, then, natural to have recourse to these lamps as secondary standards in measurements of electric photometry. An incandescent lamp furnishes light of constant intensity for quite a long time, provided that the number of watts expended in the filament remains invariable. It is easy to realize this condition by furnishing the lamp with the current from a battery of accumu- lators. It is in this manner only that we may obtain sufficient constancy without continually occupying ourselves with regulating 162 PHOTOMETRY. the current. It is easy to determine the conditions which must be satisfied by the current which supplies an incandescent lamp, designed to serve as a secondary photometric standard. As a first approximation, the luminous intensity of an incan- descent lamp is proportional to the cube of the power W expended in the filament ( 132), J=aTn By differentiating we obtain This equation enables us to calculate the variation in the lumi- nous intensity dl which corresponds to the variation d W in the energy absorbed by the filament. For an Edison lamp of 100 volts giving 16 candle power with an expenditure of 56 watts (3.5 watts per candle), the value of a is equal to about 0.00009. The value of dW which produces an error dl of 1 per cent, i.e. 0.16 candle power, is then = 0.19 watt In order that the incandescent lamp may be used as a photo- metric standard, we must be able to count on a constancy within at least 1 per cent. We must have at our disposal, in the case considered, apparatus allowing the expenditure of ' energy to be maintained constant within 0.2 watt in 56 watts, i.e. 0.4 per cent. Accumulators alone satisfy this condition. The current fur- nished by a dynamo, though having an excellent regulator, is not sufficiently constant. As to primary batteries, their electromotive force and resistance vary too much for them to be considered, while a battery of accumulators on being discharged slowly has a remarkable constancy of resistance and of electromotive force for several hours ; in certain cases its variations cannot be discovered, even with the most precise measuring apparatus. It is usual to have recourse to a low-voltage lamp, using con- siderable current, unless there is at one's disposal a battery of accumulators of 50 cells, which gives the 100 volts required for lamps of the kind most used. It is true that, if low-voltage lamps are used, the current is higher, and the constancy of the cells of the battery of accumulators is less. The measurement of the energy absorbed by the standard lamp, PHOTOMETRIC STANDARDS. 163 i.e. the simultaneous measurement of voltage and current, may be made by means of apparatus which every electrical laboratory possesses. It should not be forgotten that this measurement must be exact in order to obtain the real value of the luminous intensity. Its accuracy should be many times (at least 4 times) that which we wish to obtain in the constancy of the luminous standarl. It is useless to dwell on the experimental arrangements to be used in this measurement, for they are principally determined by the appa- ratus at hand. However, it may be well to say that the simplest arrangement for measuring the intensity of the current appears to be the measurement of the difference of potential between the ends of an invariable known resistance. It is at the same time the most convenient, since the measurement of the difference of potential between the terminals of the lamp may be made with the same apparatus. It is further the method employed by Lummer and Brodhun* in their researches on the employment of Siemens 65 volt, 16 c. p. lamps as secondary photometric standards. These investigations showed that these lamps gave a sufficiently constant light for all practical needs ; further, for quite a long period, these lamps have a sensibly constant luminous efficiency, i.e. they absorb the same quantity of energy to produce the same luminous intensity. It follows from this that the standardizing of the incandescent lamp by means of the chosen absolute standard does not need to be repeated as frequently as seems necessary on first thought. Violle Absolute Standard. 104. As a consequence of Violle's researches, the conference on electrical units adopted the proposition of this physicist to take as the photometric unit the quantity of light emitted by a determined portion of the surface of a bath of fused platinum. The resolution adopted by the Conference is as follows : The unit of each simple light is the quantity of light of the same kind emitted normally by 1 sq. cm. of surface of melted platinum, at the temperature of solidification. The practical 'unit of white light is the quantity of light emitted normally by the same source. One of the first conditions is to have perfectly pure platinum ; the presence of foreign bodies not only alters the temperature of * Zeitschr. fur Instrumentenkunde, 1890, p. 119. 164 PHOTOMETRY. fusion, but may also cause the formation of oxides tarnishing the sur- face of the bath and modifying its emissive power. Perfect purity is not difficult to obtain, and, moreover, the same platinum may serve indefinitely. To produce the fusion of platinum Violle* employed the furnace designed by Deville and Debray in their work on the metallurgy of this metal. This apparatus consists of a piece of lime hollowed out FIG. 53. Apparatus for the Reproduction of the Violle Standard. to receive the platinum and having a cover also of lime, with a blow- pipe (using illuminating gas and oxygen) passing through it ; a tem- perature well above the fusion point of platinum (1775 C.) is thus obtained. When the platinum is melted, it is brought below a dia- phragm having an opening of determined area which may be any fraction of a square centimeter ; a multiple or a sub-multiple of the absolute unit is thus directly obtained. The hollow diaphragm of copper or platinum is constantly traversed by a current of cold water. The photometric measurement should be made at the moment of solidification. Following is the manner in which Violle conducted * Lum. l, Vol. XIV. p. 475. PUO TOMETRIC STANDARDS. 165 the operation : the gas is shut off and the melted metal is allowed to cool ; the luminous intensity diminishes at first rapidly, then more slowly and next becomes stationary, only to begin again to decrease some seconds later after a Hash ; the moment of making the meas- urement is thus well determined. Figures 53 and 54 show the photometric arrangements which Violle used to compare his standard with the carcel lamp. The pho- tometer of Fig. 53 is a Rumford photometer, used in lighthouses, arranged to make the comparison with the light emitted at 45 by the melting platinum ; that in Fig. 54 is a Foucault photometer FIG. 54. Apparatus for the Violle Standard. with an automatic balance for the carcel lamp ; with this photometer is measured light emitted normally and reflected by a mirror at 45. Proceeding in this way, Violle found the absolute standard, as defined by the International Conference, equal to 2.08 carcel units. The principal objections which have been made to the Violle standard are : the complication of the apparatus, the difficulty of measuring, and the high price of the platinum, which must be employed in quite large quantities. From a practical point of view, it was evident from the first that the absolute standard would not be commonly employed; the International Conference in adopting the proposition of Violle cared more for the unification of photo- metric standards than for the creation of a unit of light directly use- ful in photometric measurements. 166 PHOTOMETRY. However, it should not be concluded that Violle gave up the introduction of his apparatus into industrial practice ; but while the practitioners who sought to simplify the absolute standard have employed very small masses of platinum, thus sacrificing exactness to convenience, Violle has aimed to obtain an apparatus industrial and at the same time fulfilling the promises of exactness of the original apparatus. Simplified Model of the Violle Standard. 105. According to the plans of Violle, Carpentier constructed the apparatus of which Fig. 55 gives the perspective. The fusion of platinum is obtained by the combustion of illuminating gas in FIG. 65. Violle Standard (Simplified Form). oxygen and takes place in a crucible of lime. This crucible is com- posed of two parts : the lower part has a cavity in which the ingot of platinum is placed ; the upper part serves as a cover, and is also hollowed out to correspond to the lower part. The two blocks of lime of the lower and upper parts of the crucible are mounted in iron; the cover of the crucible has a circu- lar channel D which serves to carry the gas. This channel has two PHOTOMETRIC STANDARDS. 167 concentric tubes d and d' ; the inner tube corresponds to the tube , bringing oxygen, and the exterior tube corresponds to the tube G ; through which the illuminating gas comes. The valves admitting the gases are operated by two concentric ; rods which are moved by means of the buttons T and T'; each of these rods works a rack which gears with a toothed sector in which the valve terminates. When the platinum is melted, the cover is gently raised from the crucible by pressing on the handle P and moved to one side by turn- ing it about the axis A by means of a lateral pressure on the handle P. We then give to the crucible C a gentle movement back and forth by oscillating the crank M which works the rack F; in this way it is ascertained whether the fusion of the platinum is complete and the surface perfectly clear. By turning the crank M, the cruci- ble is then brought under the screen E. This screen of copper has a circular opening 1 sq. cm. in area; it is hollow in order that a current of cold water, carried by the tubes R and R f , may keep it from becoming too hot. The quantity of light emitted by the surface of the platinum, at the instant of the solidification of the metal, and which traverses the opening of the screen, is then exactly equal to the absolute unit of light. The mirror M, which may be regulated by: means of a rotation about two axes perpendicular to one another, serves to reflect the light in the desired direction. The oxygen necessary for the fusion may be obtained in the ordi- nary manner in proportion as it is needed ; but this solution, which is quite acceptable in a laboratory, is not at all practicable for common use. For the latter, it is simpler to employ the oxygen under pres- sure, which is now to be obtained at a comparatively low price. This oxygen is stored in cylinders under a pressure of 50 atmos- pheres ; as the pressure of the gas on leaving the pipe does not exceed that of a few centimeters of mercury, the pressure of the oxygen should be reduced to the same value. This reduction of pressure is obtained by means of a special regulator fitted to the cylinder. An ordinary cylinder about 0.30 m. in diameter, and 1.50 m. in length, suffices for a great number of measurements. Thus Violle used the same cylinder for the numerous tests which he made for the benefit of visitors to the photometry room, at the Exposition of 1889. 168 PHOTOMETRY. The crucible is very easily manipulated, and its installation pre- sents no difficulty. It is sufficient to have a gas connection near by, and to have at one's disposal a cylinder of oxygen. It is put into operation very rapidly, and the fusion of a block of platinum of 1 kg. is obtained in about a quarter of an hour. It is known that the absolute unit of light is obtained at the moment of solidification of the platinum ; this is indicated in a pre- cise manner by a characteristic flash which is produced regularly and surely when a mass of platinum of about 1 kg. is employed ; it cannot ba attained with the same regularity and the same certainty if the mass of platinum is much smaller. This flash is very well observed directly; it is still better appreciated on the photometer by following the variations of the light emitted by the standard up to the time when it emits its flash ; it is the reading which is made at this exact moment which should be counted. The latter is ob- tained very surely with a little experience, for it is determined instinctively by a comparison of the observations made immediately before the solidification with those made immediately after. The reading made, it is sufficient to replace the crucible under the oxyhydrogen flame; complete fusion is again obtained at the end of several minutes, and a new measurement may be commenced. A condition essential to exactness of the measurements is the absolute purity of the metal in fusion and the complete absence of films on the surface of the liquid metal. When these appear, they are removed either mechanically or by a chemical reduction. The great importance of the platinum standard is a consequence not only of its constancy, and the fact that it can be exactly reproduced each time, but also of the quality of its luminous radiations. From the point of view of electric photometry in par- ticular, the composition of the light of the absolute standard is comparable with that of the light of incandescent lamps under ordinary circumstances and, although in a less degree, with that of the arc-light. The photometric investigation of the arc-light can only be made with exactness when the composition of the light emitted by the source compared sufficiently resembles the voltaic arc; for this reason the platinum standard in the industrial form appears des- tined to render considerable service to electric photometry, especially as this form of the apparatus is still susceptible of considerable simplification. It is sufficient, in fact, to apply to the fusion of platinum the PHOTOMETRIC STANDARDS. 169 processes of electric fusion in order to simplify not only the appa- ratus, but especially its installation and manipulation. Electricians would familiarize themselves much more rapidly with the platinum standard were they not obliged to have recourse to oxyhydrogen fusion, for electric fusion may be effected rapidly and easily with the resources of every well-equipped electro-technical laboratory. As electric fusion takes place generally by means of very intense currents, it would be easiest to employ the current furnished by a battery of accumulators charged in series and discharged in parallel. The Violle-Siemens Standard. 106. W. Siemens sought to attain the legal standard in such a way as to satisfy the requirements of practice while conforming as much as possible to the legal definition. However, the simplifi- cation attained by Siemens was at the expense of exactness, in this way that the apparatus does not exactly fulfil the conditions which the International Conference resolved upon. The platinum is taken at its point of fusion and not at its point of solidification. It is not known for certain whether there exists any difference between the points of fusion and solidification of platinum. As to the constancy of the light emitted at this moment, it has not been perfectly proven ; thus Cross has observed that the luminous intensity is somewhat greater if one employs platinum which has been melted many times; the influence of this is insen- sible on the point of solidification, which is an additional argument in favor of Violle's method. Figures 56 and 56 bis represent horizontal and vertical cuts of the apparatus ; it consists essentially of a small metallic box, one of whose sides is pierced with a conical opening; the surface of the smallest circle measures exactly one-tenth of a square centimeter. Immediately behind this window there is a very thin (0.02 mm.) ribbon of platinum 5 or 6 mm. in width, which extends beyond the edge of the opening in all directions. Through the platinum ribbon there is passed an electric current whose intensity goes on increasing gradually ; the brightness of the light emitted through the conical opening increases also gradually up to the instant when the platinum melts and the brightness suddenly disappears. This progressive increase in the intensity permits the operator to balance in the photometer at each instant the illuminations of the lamp studied and of the platinum standard. The quantity of light 170 PHOTOMETRY. emitted by this apparatus, at the instant of the fusion of the plati- num, is equal to a tenth of the absolute standard, i.e. about 0.2 carcel. The International Congress of Electricians of 1889 having decided to give the name of decimal candle (bougie decimate) to the twentieth part of the absolute platinum unit, the Violle-Sieinens standard has thus a luminous intensity equal to two decimal candles. A special mechanism, inside the case, managed by the handle g, is designed to bring a new ribbon of platinum before the window in place of the one which has been melted ; the experiment may then be repeated without loss of time. Liebenthal*, in the course of very extended investigations of the Siemens standard, modified to some extent the original apparatus ^ FIG. 56. Violle-Siemens Standard (Vertical Section). FIG. 56 bis. Violle-Sieinens Standard (Horizontal Section). the small metallic box K bears the metallic plate A, insulated from the frame, on which there is a coil R of platinum ribbon ; this plate bears, further, the small movable guide m, and the fixed guide M of greater size ; one of the terminals P of the apparatus is also con- nected with this plate, while the other Q is fixed directly in the side of the metallic box. The platinum ribbon, after having left the cylinder R, passes by the guides m and M, against which it is pressed by the spring /, and before the opening D whose area is exactly 0.1 sq. cm.; it is then grasped by the clamp S; a key which governs the guide m allows the tension of the platinum ribbon to be varied. * Lum. til.. Vol. XXXI. p. 116. PHOTOMETRIC STANDARDS. 171 The current brought to the terminal P enters the platinum ribbon at the guide M principally, then is conducted by the spring Z to the terminal Q. When the circuit is broken because of the fusion of the platinum, the rod g is pressed, which pushes the movable clamp S upon the plate A, where it opens ; when the rod g and the movable clamp S are drawn back, the clamp closes and draws along a new piece of the platinum ribbon to be used; with 1 gram of metal, costing about 60 cents, 50 measurements may be made. The first measurement of Liebenthal gave good enough results ; but soon quite large errors appeared, caused by irregularities in the spring /, which rested on the guide m only ; the portion of the plat- inum ribbon traversed by the current thus being longer, fusion took place near M and not opposite the opening D. FIG. 57. Violle-Siemens Standard (Liebenthal Form). Liebenthal was then led to somewhat modify his apparatus; doing away with the contact at M or at m not having given good results, a simple screw, insulated from the metal box and pressing the platinum ribbon against M, replaced advantageously the original arrangement. The guide m was also done away with, because the tension of the ribbon could be regulated well enough by the clamp S 9 and experience, furthermore, showed that the degree of tension of the platinum ribbon had only a very slight influence on the luminous power of the lamp. To obtain good contacts, the cylinder M must further be covered with a strip of platinum ; with these modifica- tions, the apparatus worked successfully from that time. When rolling the platinum on the cylinder It, care should be taken to avoid wrinkling the ribbon, for the least break displaces the point of fusion and modifies the light emitted. 172 PHOTOMETRY. Increase in the intensity of the current produces at first a rapid increase in the luminous intensity ; it then becomes slower as the instant of fusion approaches; finally, fusion takes place suddenly, and the light disappears. The last photometric setting which is made before extinction is alone valuable. Liebenthal made a certain number of comparisons with Hefner's acetate of amyl lamp, taking with the latter all the precautions enumerated above and employing a liquid carefully rectified. He found that the mean deviation of a photometric comparison between the acetate of amyl lamp and the platinum standard was about 2.9 per cent, while other measurements gave 0.-9 per cent for the mean deviation of the comparisons of the acetate of amyl lamps. These variations, as Liebenthal elsewhere remarks with justice, do not result alone from such large real variations in the luminous intensity of the platinum standard, due for instance to variations in the molecular structure and in the emissive power of the metal ; they are due in great part to the difference in color of the two sources of light. At the moment of fusion, the platinum standard emits a much whiter light than that of the acetate of amyl lamp ; the measurements are then affected by all the causes of error which render the comparison of two differently colored luminous sources so difficult. The luminous intensity of the platinum standard in terms of the acetate of amyl lamp was also determined many times by Liebenthal. He found that 1 Violle-Siemens unit = 1.757 Hefner units. Whatever may be the merits of the Siemens standard and the ingenuity displayed in the details of the apparatus, it is important not to lose sight of two principal defects. The observer must make the setting at the precise moment when fusion takes place ; now at this same moment the emission of light ceases suddenly. The photometric setting must then be made, so to speak, on the wing. Further, the Siemens standard does not exactly reproduce a tenth of the absolute standard of Violle ; for the observation is made at the moment of fusion and not at that of solidification of the platinum, which may produce a quite considerable difference with respect to the quantity of light emitted ; further, very slight lack of uniformity in the section of the ribbon and of homogeneity in the metal is enough to cause very sensible variations. PHOTOMETRIC STANDARDS. 173 107. To conclude, we give a double-entry table which sums up all the comparisons of different photometric standards made by Violle. Violle Units. Carcels. Star Candles. German Candles. English Candles. Hefner- Alteneck Lamps. Violle units . . 1.000 2.08 16.1 16.4 18.5 18.9 Carcels . . . 0.481 1.00 7.75 7.89 8.91 9.08 Star candles 0.062 0.130 1.00 1.02 1.15 1.17 German candles 0.061 0.127 0.984 1.00 1.13 1.15 English candles Hefner- Alteneck lamps . . . 0.054 0.053 0.112 0.114 0.870 0.853 0.886 0.869 1.00 0.98 1.02 1.00 CHAPTER IV. GENERAL EQUIPMENT AND AUXILIARY APPARATUS OF PRACTICAL PHOTOMETRY. 108. The preceding chapters have been devoted to the study of photometric apparatus and units of measurement. There remains to be found the best manner of arranging them for measurements and the precautions which must be taken to obtain satisfactory precision. Photometry Room. 109. In every laboratory where it is desired to make photo- metric measurements, there should be set apart a special place, judiciously chosen, and satisfying the following fundamental con- ditions. The photometry room should be large enough. It is a great error to crowd the photometric apparatus into a small room, espe- cially when photometric standards based on combustion are > used, e.g. carcel, Hefner, petroleum lamps, candles, etc. The luminous intensity of these photometric standards varies greatly with the degree of purity of the surrounding air ; it dimin- ishes in proportion as the quantity of carbonic acid gas in the air increases. For instance, at the end of an hour the products of respi- ration of two people are sufficient to vitiate the air in a large room so as to produce a very noticeable diminution in the luminous intensity. Further, the presence of lights brings about an elevation of temperature which contributes to render the measurements less exact, owing to the fatigue of the observer. This can be remedied only imperfectly in a photometer room of small dimensions by introducing a little stronger system of ventilation. Xo attempt should be made to use ventilating apparatus during the measurements themselves, for the photometric standards should be free from even the smallest currents of air. Recourse should be had to it between measurements, which, however, produces each time a disturbance in 174 GENERAL EQUIPMENT. 175 the regulation of the standard lamp. We do not know then whether the luminous intensity of the lamp returns to its initial value or not. The photometry room should have its walls painted a dull black, and it should be possible to obtain complete darkness. This con- dition is indispensable if the photometric screen is to receive only such light as comes from the two sources to be compared. It more- over permits the eye to rest in the interval between measurements. The light necessary for reading the apparatus and making notes should be furnished by lamps of small intensity, fitted with reflectors which do not allow the light to be diffused over the room. During the setting of the photometer, the observer should be shielded from luminous rays coming directly from the two sources. For this there may be used either screens or a black cloth like that used by photographers. The latter has, however, the objection that it makes the observer very warm. Personal Errors. 110. Like all measurements in which the personality of the observer enters directly, photometric measurements are affected by personal errors which may be very considerable. In a general way the personal error is proportionately less when the observed phe- nomenon is precise and leaves the observer no chance for doubt. In photometric measurements the determination of the equality of the illumination of the two parts of the screen depends very largely on the judgment of the observer, especially when there is a differ- ence in tint. From this some sensible personal errors must result ; this was discovered as soon as the exactness of photometric measure- ments permitted. This fact was proven only recently in a precise manner by Nichols*. The following is the method used by him, a method which may serve as an example for researches of this kind. Three incandescent lamps of 16 candle power at 110 volts, chosen so as to have as nearly as possible the same luminous intensity, are placed in shunt, using a battery of accumulators of 120 volts, the circuits separating beyond a rheostat which regulates the intensity of the current. One of the lamps L\ being taken as a standard, the two others, L 2 and Z/ 3 , are successively compared with it, so as to obtain the * Lum. l., Vol. XXXIII. p. 414. 176 PHOTOMETRY. ratio of their luminous intensities, ~. It is found, for instance, in this way, that i = 1.0032 0.0015. Next, while always preserving the same intensity of current through the lamps, we determine the ratio -? by directly comparing the luminous intensities of the two lamps, the lamp L 2 being placed at the right, the lamp L 3 at the left of the screen. To avoid errors due to slight variations in the intensity of the currents, the lamps studied were given 12 instead of 16 candle power; for, at this intensity, variations of current are much less felt in the luminous intensity. The ratio -? was determined by ten different observers. The fol- lowing table gives the values obtained in this manner, as well as the corresponding personal error, which was calculated by assuming as the real value of -? the quantity 1.0032, obtained by double com- parison. Each number is the mean of the results of ten different measurements ; the probable error of this mean was determined. Observer. /5 Value of - Is Personal Error. A 1.0590 0.0040 - 0.0558 B 0.9701 0.0044 + 0.0331 C .0021 0.0022 - 0.0189 D .0191 0.0072 - 0.0159 E .0182 0.0039 - 0.0150 F .0902 0.0057 - 0.0870 G .0733 0.0063 - 0.0701 H .0293 0.0042 - 0.0261 I .0297 0.0050 - 0.0263 J .0220 0.0027 - 0.0.188 It is then seen that the ratio -? was found by all the observers, *8 except one, greater than 1.0032, the value obtained by indirect com- parison which eliminates personal errors. The personal error of the ten observers, then, varies between 0.0870 and -f 0.0331 ; i.e. between 8 p?r cent and + 3 per cent. GENERAL EQUIPMENT. 177 111. These measurements were made by means of the Bunsen photometer, having two lateral Kudorff mirrors. The observer viewed the two images of the spot, the left image with the left eye, the right image with the right eye. Nichols assumes that in this case the personal error is due in a great part to a difference in sensitiveness of the eyes of the observer ; the latter then judges that the screen is at too great a dis- tance from the lamp whose rays fall directly on the side of the spot which is observed by the less sensitive eye. According to this explana- tion, the right eye must have been more sensitive than the left for the nine observers who had a negative personal error, while the inverse must have been true for the tenth (B) . Afterwards some observations were made with one eye, the other being blind-folded ; these observations became more difficult, but on the other hand more sure, and likewise the observer felt more confi- dence in them. Further, the results obtained with the left eye were identical with those obtained with the right. Thus the values obtained by the observers A and B, which differed at first by 8 per cent, are absolutely concordant when only one eye at a time is used in the observations. Below are some significant figures : Observer. Eye. /2 h Personal Error. A Eight. 1.0028 0.0010 0.0004 A Left. 1.0001 0.0019 0.0031 B Right. 1.0001 0.0017 0.0031 B Left. 1.0031 0.0018 0.0001 The preceding shows then that the personal error is far from being a negligible quantity in photometry; the only means of remedying it is to employ photometers which allow monocular observations. 178 PHOTOMETRY. The Photometric Bench. 112. In the study of the Foucault photometer ( 20), we described the complete equipment and the apparatus for measuring and regulating the distances c^ and d 2 of the radiants from the screen. We did the same for the Bunsen photometer ( 24). It is, however, proper to add to these descriptions, for the photometric bench is an essential part common to the majority of the numerous photometric apparatus which we have described in the second chapter. The photometric bench is an optical bench strongly and carefully constructed. Its object is to permit the measurement of the distances d 1 and d 2 from the screen to the two radiants. It has a divided scale on which the positions of the screen are read. In the majority of cases, the two lights to be compared are fixed at the ends of the bench, and the reading is effected by moving the screen alone. This method is the most advantageous, as the observer regulates at will the position of the screen so as to obtain the most precise setting. The intensity of the standard being I 19 that of the source studied J 2 , we have the equation, The length of the photometric bench being represented by I, and the distance di from the screen to the standard by x, we have d 2 = / x, and the preceding equation becomes _ It is advantageous to calculate a table of values of the fraction { " ~ X ' for the length I of the photometric bench employed. This 3/ table may be calculated for values of x varying from millimeter to millimeter in the parts of the bench most frequently used. 113. The table of values of the coefficient ~ x is of great service in the standardizing of incandescent lamps. It is well GENERAL EQUIPMENT. 179 known that there should be determined for each lamp the voltage which really corresponds to the nominal luminous intensity. The lamps are then classified according to their voltage. There is employed as a photometric standard an incandescent lamp whose voltage is maintained constant and whose corresponding luminous intensity is exactly known. Let us assume that the lamp to be studied should give a lumi- nous intensity of J 2 candles. This intensity will really be obtained when the screen occupies on the photometric bench the division x determined by means of the equation whence x j=- 1 + \r * -*2 A single example will suffice to show the use of this formula. Let us suppose that the standard /j gives 12 candles at 65 volts. What position must be given to the screen in order that the lamp studied may give 16 candles at the moment when the photometric setting is exact? Let us assume that we have I = 300 cm., which is a very prac- tical value. We shall have x = = 139.5 cm. We may calculate a table for x in terms of the ratio y and for the length of bench used. Following is a table of this kind calculated for I = 300 cm. The table is arranged as usual with the tens in the left-hand vertical column and the units in the top row. In the numerical example preceding we had 5 = =| = 1.33. Looking up 1.33 in the table, we find a =139.3. Jl U 180 PHOTOMETRY. X. l 2 3 4 5 6 T s 9 50 25.0 23.8 22.7 21.7 20.8 19.8 19.0 18.2 17.4 16.7 60 16.0 15.4 14.7 14.2 13.6 13.1 12.6 12.1 11.6 11.2 70 10.8 10.4 10.0 9.7 9.3 9.00 8.69 8.39 8.10 7.83 80 7.56 7.31 7.07 6.84 6.61 6.40 6.19 5.99 5.80 5.62 90 5.44 5.27 5.11 4.95 4.80 4.66 4.52 4.38 4.25 4.12 100 4.00 3.88 3.77 3.66 3.55 3.44 3.35 3.25 3.16 3.07 110 2.98 2.90 2.82 2.74 2.66 2.59 2.52 2.45 2.38 2.31 120 2.25 2.19 2.13 2.07 2.01 1.96 1.91 1.85 1.80 1.76 130 1.71 1.66 1.62 1.58 1.53 1.49 1.45 1.42 1.38 1.34 140 1.306 1.271 1.238 1.205 1.178 1.142 1.113 1.083 1.055 1.027 160 1.000 0.974 0.948 0.923 0.899 0.875 0.852 0.830 0.808 0.787 160 0.765 0.745 0.726 0.706 0.688 0.669 0.652 0.634, 0.617 0.601 170 0.585 0.569 0.554 0.439 0.524 0.510 0.496 0.483 0.470 0.457 180 0.444 0.432 0.420 0.409 0.397 0.386 0.376 0.365 0.355 0.345 190 0.335 0.326 0.316 0.307 0.298 0.290 0.282 0.273 0.265 0.2o8 200 0.250 0.243 0.235 0.228 0.221 0.215 0.208 0.202 0.196 0.190 210 0.184 0.178 0.172 0.167 0.161 0.156 0.151 0.146 0.141 0.137 220 0.132 0.128 0.123 0.119 0.115 0.111 0.107 0.104 0.100 0.096- 230 0.093 0.089 0.086 0.083 0.080 0.076 0.074 0.071 0.068 0.065 240 0.063 0.060 0.057 0.055 0.053 0.050 0.048 0.046 0.044 0.042 250 0.04 0.038 0.036 0.035 0.033 0.031 0.030 0.028 0.027 0.025- 114. To conclude, we give a description of the photometric bench of the Physico-Technical Institute of Berlin, which was used in the researches of Lummer and Brodhun. It consists of two steel bars more than 2 m. in length; these have a thickness of 25 mm., a height of 50 mm., and the distance between them is about 100 mm. Under these circumstances bend- ing of the bench is not to be feared. Three cars roll on these bars with a very easy movement. They may be stopped by means of a lever in any position on the bench. Each of them has a vernier which reads to about 0.3 mm. on the millimetric divisions engraved on the upper face of one of the bars. The body of each car consists of a rather thick metallic sheet with an opening in which a steel tube may be moved vertically. On these tubes are fixed the photometric box and the supports of the two luminous sources respectively. Care is then taken to regulate each vernier so that its zero may coincide with the axis of the vertical tube. Further, the car of the photometric box has an arrangement GENERAL EQUIPMENT. 181 which allows it to be moved rapidly 2 or 3 cm., which is indis- pensable for verifying the exactness of the photometric setting. Benches planned for industrial measurements need not neces- sarily be constructed with so great care; but they should comply to some extent with the principal conditions mentioned above. Equipment of the Photometric Laboratory. 115. It is not possible to give in advance plans and details for the equipment of a laboratory of photometry, for they depend too much on the object for which the laboratory was built. There is in this regard a fundamental difference between a laboratory for research or for instruction, and an industrial laboratory for testing. We shall not occupy ourselves with the former kind except to men- tion some remarkable installations. One of the first electro-photometric laboratories built in all par- ticulars according to a determined plan is that which served at the FIG. 58. Photometry Eoom at the Munich Exposition. tests of the Committee of Experiments at the Electrical Exposition at Munich in 1882. Figure 58 gives the arrangement of the apparatus. AB and BC are two photometric benches 6 and 12 m. in length, respectively, on which may be moved the Bunsen screens a, b. The standard adopted was the candle, with various intermediate standards, e.g. the candle-burner (bee-bougie) of Giroud, shown at II, regulating the Argand burner at III, and an intensive Siemens burner shown at V. The Argand' burner served to measure incandescent lamps placed at IV, and the intensive Siemens burner to measure arc- lamps placed at VI. The supply of the three gas-burners was meas- ured by three meters G 2 , G 3 , G 5 regulated by the general regulator 7?. The standard candle is placed at II, the incandescent lamp at I, and a large petroleum lamp occupies the place of the Siemens inten- sive burner at V. The arrangement of the various intermediate standards shows th > order in which the measurements should be made. First the candle- 182 PHOTOMETRY. burner II is compared with the candle I, then the candle-burner II with the Argand burner III ; and, finally, this last with the incan- descent lamp IV. The light sources II, III, IV burn throughout the measurements. They are masked by a screen when not in use. To measure the intensity of the arc-lamp at certain inclinations, there is fixed to the end C of the photometric bench a mirror mov- able about a horizontal axis. The lamp VI is then raised to well- determined heights, corresponding to inclinations of 15, 30, etc., so that the rays may be reflected by the mirror parallel to the axis of the photometer. The striking thing about this equipment is the number of inter- mediate standards furnished by gas-burners. Nowadays one would rather have recourse to incandescent lamps. The equipment of the laboratory of the Electrical Exposition at Vienna in 1883 only differed from that at Munich by doing away with the gas-burners employed as intermediate standards. At Philadelphia, the committee of the Franklin Institute, em- ployed with the greatest success the Methven screen (Fig. 48) com- bined with a burner of the Argand type, while at Antwerp, as at Paris in 1881, use was made of the carcel lamp. For arc- lamps, however, an intensive Siemens bur- ner was used at Antwerp as an intermedi- ate standard. Figure 59 shows the equipment of the photometry room used by the Committee on Tests at Antwerp. This room was divided by a partition BBB of black cloth. The photometric bench P served to com- pare the arc-lamp L with the Siemens burner placed at S ; a second bench placed at P' served to measure the intensity of the Siemens burner in terms of the carcel standard. Observations were made simul- taneously with both apparatus. Among the number of best equipped laboratories of photometry should be cited the one which D. Monnier installed in 1883 for the Association for the Study of Electricity, formed by the principal French gas companies. The photometric part of this laboratory is provided with the latest apparatus. An industrial laboratory for testing does not necessarily include L. FIG. 59. Photometry Room at the Antwerp Exposition. GENERAL EQUIPMENT. 183 all the apparatus of a laboratory for investigation or instruction, but the general plan remains the same as that which is given above, if the measurement of the luminous intensity of arc-lamps is to be included. If measurements are restricted to incandescent lamps, the equipment may be considerably simplified. The choice of the photometric screen is very important. Up to the present, the Foucault screen and the Bunsen screen have had the preference. But the Lummer and Brodhun screen is much superior to them and ought to be adopted as far as possible. As to auxiliary apparatus, there is room for choice among those whose description will follow. Dibdin's Radial Photometer. 116. Arc and incandescent lamps emit quantities of light varying with the direction of the luminous rays ; this variation is much greater with these than with ordinary gas-lights. Therefore it is of the greatest importance to be able to measure the intensity of a radiant in any direction. Attention was called to this for the first time by Allard in his memoir on the intensity and range of lighthouse beacons. The method which presents itself is to turn the entire photometric bench so as to place it in the direction of the luminous rays. It is this which Ayrton and Perry ( 39) realized in their disper- sion photometer. Weber's photometer ( 52) also realizes this condition. The apparatus, being movable about a vertical axis, may be turned in any azimuth. As the tube which serves to determine the direction of the photometer from the light studied is movable about a horizontal axis, it follows that it may be set equally well at any inclination. Ordinary screens, the Bunsen screen for instance, may, however, be employed for the measurement of the inclined rays, account being taken of the fact that the illumination of the screen does not depend on the distance alone of the luminous sources, but also on the angle of incidence of the rays which fall on the screen. Natu- rally account should also be taken of the loss of light due to absorp- tion and reflection ; this loss increases with the angle of incidence of the rays. Dibdin found, for instance, that for the Bunsen screen which he employed it was: 184 PHOTOMETRY. 5% for an angle of incidence of 22.5. 12 " " " * " " 45. 68 " *' " " " " 67.5. Unfortunately these numbers are only of value for Dibdin's particular screen, and should be determined anew in each particular case. This correction may be eliminated by so placing the photometric bench that the rays strike the two sides of the screen at the same angle. Hartley * first proposed to make the screen movable about an axis, so as to place it always in the bisecting plane of the dihedral angle formed by the two radiants and the photometer. Dibdin realized this arrangement in the radial photometer f, the arrangement of which is given in Figs. 60 and 61. T, IT* FIGS. 60 and 61. Dibdin's Photometer. Upon a horizontal base rest two vertical guides ; the guide 2\ is fixed and carries the light to be studied ij on a block movable in a slot. The guide T 2 , which may be moved horizontally, supports at P the photometric screen. The two guides further carry two arms which are hinged at O x and 2 . The arm B has an index which shows on a divided circle at Oi the angle which the rays from Zq falling on the photometric screen make with the horizontal. At 2 there is further a sector divided into half-degrees. To make a measurement, the index of the screen is placed on the division of 2 which corresponds to the *Lum. til., Vol. X. p. 58. t Lum. til., Vol. XXX. p. 227. GENERAL EQUIPMENT. 185 number on 0\. The photometric standard L 2 is supported on the divided arm _B 2 , along which it may be moved at will. The length of the arm BI being constant, the distance of the radiant L from the screen P is invariable, so that the arm B 2 may be graduated directly in candles. Dibdin's radial photometer may be simplified by making the movements of the screen depend on those of BI and B 2 , so that the screen is always placed in the bisecting plane of the angle formed by BI and B z . This simplification is obtained in the appa- ratus shown in the preceding figure by means of the articulations EF and OF. The graduated sector 2 may then be omitted. Rousseau's Radial Photometer. 117. At the time of the photometric measurements of the arc- lamps exhibited at Antwerp in 1885, Rousseau * invented an appa- ratus which is much like that of Dibdin, but which provides for the employment of the Rumford photometer. Below is a description of this apparatus (Fig. 62). The lamp A is suspended between two uprights, and a mechanism operated by the crank W enables it to be raised and lowered. On these uprights there is also fixed a circular box E ; from the center of this box two rods diverge, one, G, horizontal, the other, F, inclined, each carrying a movable mirror JVand M. At the center of the box E is found a white screen 0, carried on the rod OH-, this forms one of the diagonals of an articulated quadrilateral OKHI, so that the screen always makes equal angles with the direction of the rods G and F. When it is desired to use this apparatus, the lamp A is placed behind the graduated circle E, so that the light is opposite the cen- ter 0, and at a distance as small as the form of the lamp studied will permit. The light emitted by this source is reflected by the mirrors M and N (cut from the same glass), which project on the white screen the shadows of the two rods ra and n, also fixed on the rods G and F. One of the mirrors being fixed, the other is moved in or out until equality of the shadows projected is obtained. Kru'ss has constructed a model of Rousseau's photometer com- bined with a Bunsen screen, for the use of those who prefer this photometer to that of Rumford. This model is made with great * Comptes rendus des travaux de Comite Internationale des essais electrique de V Exposition d'Anvers, p. 85. 186 PHOTOMETRY. care ; it possesses, in particular, an arrangement which allows one to determine quickly whether the voltaic arc is accurately centered with reference to the apparatus or not. . S ^ FIG. 62. Rousseau's Photometer. Vernon-Harcourt's Holophotometer. 118. This apparatus * is based on the employment of the Bunsen screen combined with a system of mirrors, planned so as to avoid errors due to the movements which the lights compared undergo. What characterizes this apparatus is, that the lamp to be measured and the system of mirrors are not placed on the photometric bench, * Lum. til, Vol. XXIX. p. 286 ; Elect. Rev. (London), July 13, 1888. GENERAL EQUIPMENT. 187 but on a table or on independent supports ; the screen alone is mov- able on the photometric bench. The apparatus is composed of two mirrors, the larger of which (Fig. 63) is clamped at the end of a horizontal axis carried by a support B ; the center of the mirror corresponds to the center of the axis, but the mirror may be inclined at any angle. This axis is placed at the height of the Bunsen screen and in the direction of the axis of the photometer. At the other end of this axis (which is not shown in the figure) is hinged a sliding arm carrying at its end a FIG. 63. Vernon-Harcourt's Holophotometer. small mirror. By this arrangement it is seen that the two mirrors always turn together about the axis of the photometer, and these rota- tions are read on the divided disc, which, further, serves as a screen and avoids having the direct rays from the lamp to be studied fall on the Bunsen screen. Figures 63 and 64 show the apparatus arranged for the measure- ment of the horizontal rays from the lamp L placed behind and masked by the divided circle. Figure 65 shows the arrangement of the apparatus to measure vertical rays. It is evident from the con- struction that when once the rays have been adjusted along the axis 188 PHOTOMETRY. of the photometer they will remain there for all positions of the arm A y taking with them the horizontal axis of the mirror M. We may thus make all the relative measurements of the luminous intensity at a given angle; to make an absolute measurement, we commence by comparing the horizontal rays emitted by the lamp L both with and without the system of two mirrors, very easily removed FIGS. 64 and 65. because of the arrangement of the support; there is thus obtained the factor of reduction by which the intensities found must be multi- plied to compensate for absorption ; naturally, account should be taken, in the measurements, of the increase in the distance due to the various reflections of the rays. Preliminary measurements showed that the absorption by the two mirrors was only 1.8 per cent. [See Appendix D.I GENERAL EQUIPMENT. 189 Millis's Arrangement. 119. Millis replaced the reflecting mirror by a total reflection prism, while using the ordinary photometric bench and the Bunsen screen. Figure 66 shows the general arrangement of the apparatus in the plan and elevation. The electric lamp is placed on its support at b and &', while at p and p' there is a total reflection prism. This prism is mounted at the end of a copper tube fixed on a tripod ; the tube has a plumb-line. The perpendicular faces of the prism must be large enough (13 sq. cm. at least). The prism may be moved about three axes which inter- sect at the middle of the principal edge; because of this arrangement the point remains fixed, regardless of the various rotations which may be given to the prism by means of screws. A pointed rod may be so placed that, when put in place of the prism, its point occupies exactly the point where the middle of the principal edge of the latter was found. To make measurements, we first find the foot b' of the vertical line passing through the lamp, and lay off from this point a line of length b'c determined by the angle at which we wish to measure the luminous intensity of the lamp. Next, a cord is stretched from b to c, and the tripod, with its copper point fixed in the support, is moved until the point touches the cord. From the point p' deter- mined by the plumb-line a perpendicular is drawn to b'c, and the photometric bench is so arranged that its axis passes through this perpendicular. It is necessary to adjust the prism until the rays which come from the source studied are reflected parallel to the photometric bench. We should then determine the correction to be applied to the measurements in order to take account of absorption of light by the prism. FIG. 66. 1 90 PHO TOMETR Y. The Employment of Mirrors. 120. The preceding apparatus permits photometric comparisons to be made at any angle. It is, however, not absolutely necessary to have recourse to special apparatus ; most frequently the ordinary photometric bench may suffice, care being taken to employ a mirror reflecting the rays from the source studied horizontally upon the screen. It is this method which was adopted by the Committee on Tests at Munich. The mirror must be movable about a horizontal axis, and its incli- nation must be easily measured on a divided circle. As the rays coming from the source make an angle a with the normal to the mirror, it is necessary, in order that they may be reflected in a horizontal direction, that this angle a should be exactly half of the angle formed by the rays with the horizontal. This angle is calculated in advance by measuring the height h of the light above the axis of the mirror and its horizontal distance d to the mirror. It follows that tan 2 a = - ; it is then sufficient to d place the mirror at the division a of the divided circle in order that the rays from the source may be reflected horizontally. In order to vary the angle a, i.e. the inclination at which the luminous intensity is measured, we may suspend the source studied by a cord and elevate and lower it at will, or, again, increase or decrease the distance of the mirror from the foot of the perpendic- ular passing through the source. This arrangement is satisfactory if the source can be placed verti- cally above the axis of the photometer. But this is not always the case. The mirror should then be movable about a vertical axis also. The angle of rotation about the vertical axis corresponds to the azimuth A, while the angle of rotation about the horizontal axis corresponds to the height 7i. We have then, by formulae of spherical trigonometry, as the condition for the reflected rays being horizontal, cos 2 a = cos A cos h. The following arrangement may also be recommended. A hori- zontal axis R is placed parallel to the axis of the photometer and above it. There is then fixed on this axis a movable arm to which is suspended the radiant, an arc-lamp for instance [the arc being at the same distance below the point of suspension as the photometer axis is below the axis of the arm]. The point of attachment of the GENERAL EQUIPMENT. 191 arm is directly above the mirror. Turning this arm, the radiant describes a portion of a circumference of which the mirror occupies the center. The mirror remaining fixed, the distance from the radiant is invariable. Sautter and Lemonnier also employed advantageously the follow- ing arrangement. The arc-lamp is placed on a support movable about a vertical axis, opposite a divided scale on which an index shows exactly the height of the axis. The mirror is fixed on a divided rod and is movable about a horizontal axis. It has an index which allows the determination of the inclination of the mirror by a simple reading on the rod and an easy calculation. All the 'preceding apparatus call for the employment of one or more mirrors. Before using them, the loss of light due to absorption of the mirror should be determined ; that is, we should determine the coefficient of reflection at different angles. This measurement is made most easily in the following way. By means of the ordinary photometer, we compare the luminous intensities of two radiants as constant as possible ; for instance, two petroleum lamps or two incandescent lamps. We thus obtain the ratio . Next, the same determination is made by means of the 0/1 1 mirror, and another ratio is obtained. The coefficient of reflec- 2 a tion of the mirror is then a = , and the loss by absorption is a i represented by the expression (1 a). All the results obtained with the mirror should then be multiplied by the factor - Below are some values obtained by Sautter and Lemonnier, using a silvered mirror, and others obtained at the Munich Exposition in the same way. Angle of Incidence. Sautter and Lemonnier. Munich. a. a. 5 0.68 .... 10 0.74 0.700 15 0.81 0.690 20 0.85 0.696 25 0.85 0.700 30 0.85 0.695 40 0.696 192 PHOTOMETRY. Recent measurements by Uppenborn confirm these results and show in particular that absorption depends in a sensible manner on the angle of incidence ; it is necessary then to determine the coeffi- cient of diminution of a mirror for the various values of the angle of incidence at which it is employed. Incandescent Lamp-Holders used in Photometry. 121. It is also indispensable to measure the luminous intensity of an incandescent lamp in several directions ; however, we usually con- fine ourselves to making these measurements in the same horizontal FIG. 67. Rousseau Support. plane for various azimuths, the variations of the horizontal intensity being as much as is generally desired. Many pieces of apparatus have been invented to facilitate these measurements. Below is the description of that which the Com- GENERAL EQUIPMENT. 193 mittee on Electrical Tests used with great success at the Antwerp Exposition. It consists (Fig. 67) of a board fixed vertically at one of the ends of the photometric bench parallel to its axis. Against this board rests a circle divided at intervals of 22. 5 by notches with which a projection on a flexible spring, which is tangent to the circumference of the circle, may engage ; this circle is movable about a horizontal axis passing through its center and supported by the board. At the center of the circle is fixed a tube of three branches D, E, F, the first and the last being parallel to the plane of the circle, the second perpendicular ; the support of the lamp is adjusted in the tube G, which may be clamped in the other tube. The lamp may be set and fixed by a screw-clamp, so as to be exactly opposite the center of the grad- uated circle; the tube G, and conse- quently the lamp, may be turned about the axis of the filament. The movable tube has a fixed index perpendicular to this axis, serving to measure the angle of rotation on a divided circle ; the latter has further a stop which allows the lamp to be fixed during the measure- ments, in any azimuth. Heim also invented a small support which has been slightly modified by Krtiss so as to avoid having the support ever placed in the path of the rays. Figure 68 gives a view of this apparatus which is placed vertically on the photo- metric bench by inserting the block A in the slot of the bench. The index Z serves to indicate the position of the apparatus. The support B may be moved vertically, but it is not movable about a vertical axis. This arm carries at c the horizontal axis about which the lamp may be turned through an angle read on the circle TTby means of the index J. On the axis c is fixed an arm D on which rests the base E to which the lamp is fixed. This base may be turned at will and tho angle read on the disc G which turns in front of the fixed index i. FIG. 68. Heim-Krliss Support. * 17 1R SIT 71 194 PHOTOMETRY. Whatever be the position given the lamp, the point ra always remains fixed; that is, it is at the same height and at the same distance from the screen. FIG. 69. Franklin Institute Support. During the duration tests of incandescent lamps, the Commission of the Franklin Institute employed a support shown in Fig. 69 which resembles in the main that of Rousseau. The notches are fixed and arranged so as to make the measurements at intervals of 22.5. CHAPTER V. ELECTRIC LIGHTS. A. INCANDESCENT LAMPS. The Principle of Incandescent Lamps. 122. When a conductor whose electric resistance is R is trav- ersed by a current of intensity /, the quantity of heat developed in this conductor during the time t, according to Joule's law, is equal to EIH gE' g being the acceleration due to gravity, and E the mechanical equiva- lent of heat. When the constants R and I are sufficiently great, the quantity of heat developed may be sufficient to raise the conductor to incan- descence. It is not difficult to deduce the differential equations of the problem in the simplest cases, by taking account of the loss of heat, but this mathematical work is of no use from a photometric point of view. The incandescent lamp comprises then a conductor consisting of a carbon filament which offers great resistance to the current ; it is so arranged as to stand the action of a high temperature without disintegrating. The luminous intensity of the filament depends on its temperature, its surface, and its emissive power ; by increasing the last we increase the efficiency of the lamp, that is, the quantity of light which corresponds to a determinate expenditure of energy. It is this increase in emissive power which has above all been realized in the improvements which the incandescent lamp has undergone during the last ten years. The emissive power of the filament is increased by covering it with a brilliant deposit of carbon, for it has been found that fila- ments whose surface is a dull black have a smaller efficiency than those whose surface is bright ; filaments with a bright surface are 195 196 PHOTOMETRY. obtained by maintaining them at high temperature in the vapor of a hydrocarbon having a high boiling-point. This process of supple- mentary carbonizing of the filaments is used nowadays by the majority of manufacturers. Manufacture of Incandescent Lamps. 123. Vacuum incandescent lamps are the only ones which have come into common use * ; there is not space here to discuss systems based on the incandescence of carbon or of platinum in the open air, these systems never having left the experimental stage. As early as 1841 de Moleyns patented in England an apparatus for the production of light by the incandescence of a platinum wire in a closed glass globe, and in 1845 King received patents relating to an incandescent carbon lamp invented by Starr of Cincinnati. There should next be mentioned the works of de Changy (1858), of Lodyguine (1873), and of Konn, Swan, etc. But it was Edison who constructed industrially the first incandescent lamp (1880) which was really satisfactory and commercial. Electric lighting by incandescence has then been in existence only twelve years; nevertheless incandescent lamps have already arrived at a satisfactory degree of perfection, owing to the numerous systematic investigations of which they have been the subject. In particular the photometric investigation of incandescent lamps has been pushed very far, which has, moreover, enabled manufacturers to modify with advantage their methods of manufacture. Every incandescent lamp consists of a carbon filament fixed to two platinum wires, a glass bulb in which a vacuum is formed, and finally a threaded base attached to the bulb and designed to hold the lamp in its socket. The following is, in a general way, the method by which incan- descent lamps are now made. The bulbs are blown at the glass factory whence the manufac- turers obtain them directly ; the first manipulation consists of pre- paring them for the filament. The nature of the filament varies with different systems ; there are three kinds principally employed. Some manufacturers take cot- ton thread (Swan), others gelatine or vitrified cellulose (Khotinski, * [There are now, 1894, in the market, several lamps for which it is claimed that the vacuum has been replaced by an atmosphere of gas which keeps the filament in good repair. Trans."} ELECTRIC LIGHTS. 197 Xiane-Fox) ; still others use vegetable fibers (Edison, Siemens) ; finally, some employ a natural fiber submitted to a chemical process (Langhans, Cruto, Seel). Definite form is given to the filament according to its nature, either by means of a die, or between cylin- ders, or by cutting it out while in a plastic mass. The fiber thus obtained is transformed into compact carbon by prolonged baking at a high temperature in a crucible, or by heating with the electric current itself. To give the filament homogeneity and the desired resistance, a layer of carbon should be deposited on its surface ; this deposit is effected in many different ways, which are peculiar to each manufacturer. A very simple method consists in immersing the filament in petroleum and raising it to a red heat in the liquid. The filament being cut to the desired length, Edison clamps the carbon with platinum wires, and covers the points of attachment with a layer of electrolytic copper ; Lane-Fox and Swan deposit a greater quantity of carbon there, while other manufacturers employ a special cement. Soldering to the carbon tends just now to become more and more employed. The filaments may be fixed in the bulb in two ways : either the two wires are fused into a piece of glass called the bridge, which is next fused into the neck of the bulb ; or else the wires are fixed sep- arately on the edges of a glass socket, which is then fused into the bulb. A small tube is also fused to the top of the bulb, in order to provide for the production of a vacuum. The exhaustion of the lamps takes place by means of mercury pumps. Sprengel pumps are almost exclusively employed. The vacuum obtained, the lamp is tested; then the luminous intensity and the resistance when cold, are measured. The bulb is not mounted until it is about to be shipped. The dimensions of the filaments vary naturally with the lumi- nous intensity of the lamp ; they should be proportionately greater as the normal luminous intensity of the lamp is higher. These dimensions depend also on the specific resistance of the carbonized substance. As to the form of the section of the filament, the circu- lar one is preferable, because it presents the minimum resistance for a given surface. In Edison lamps the filaments have a section 0.3 mm. by 0.1 mm. ? and a length when straightened out of 125 mm. for 16-candle-power lamps, and 110 mm. for those of 10 candle power. In the Maxim lamp of 16 candle power, the section is 0.5 mm. by 0.1 ram., and the 198 PHOTOMETRY. length straightened out 113 mm. The filaments of the Siemens lamps have circular sections whose diameters are 0.15 mm., 0.20 mm., and 0.27 mm. for lamps of 10, 16, and 25 candle power, respectively. The lengths of the filament for the same lamps are 110, 125, and 145 mm., respectively. The Luminous Intensity of Incandescent Lamps. 124. It is not possible to establish for all incandescent lamps the general law according to which the luminous intensity varies with the direction of the ray, for this law depends above all on the form of the filament, which varies greatly in different lamps ; for instance, the filament of the Edison lamp has the form of an inverted U, that of the Swan lamp, a horizontal buckle ; in the Maxim lamp, the filament is in the form of an M, while in the Westou lamp it is wound in a spiral about an arc of the shape of a horseshoe ; the fila- ment of the Gerard lamp has the form of an acute angle supported on the base of the bulb ; that of the Bernstein lamp of great inten- sity has also this form ; while other types of the same system have a filament in the form of an inverted A. The investigation of the distribution of luminous intensity of an incandescent lamp is very complex. The form of the filament pro- duces a sensible want of symmetry in the distribution of luminous intensity, which varies not only with the inclination of the ray, but also with its azimuth. Horizontal Intensity. 125. Supposing the lamp to be vertical, it is the horizontal intensity which is usually desired. Variations in the horizontal luminous intensity depend essentially on the form of the filament. The horizontal intensity is principally characterized by the value of the mean horizontal intensity. It is known that the determina- tion of this element necessitates the measurement of the horizontal luminous intensity at a great number of different angles at equal intervals. The mean horizontal intensity is then the mean of the values thus obtained. In practice it is well to make the measure- ments at intervals of 22. 5, and then to calculate the mean of the six- teen results. Frequently intervals of 30 or 45 may be sufficient. 126. Even this calculation may be considerably simplified by taking account of the following fact, which is true for the majority of incandescent lamps. For all lamps of a given system, we may ELECTRIC LIGHTS. 199 obtain the value of the mean horizontal intensity by multiplying the horizontal intensity, measured with the photometer bar at right angles to the plane of the filament, by a factor of reduction (7 , which is the same for all lamps of this system; this factor C varies between 0.8 and 0.9. The same result is reached by multiplying the horizontal intensity measured in the perpendicular plane by a factor Ci. Finally, the same thing was calculated at the Paris Exposition in 1881, by multiplying the horizontal intensity, meas- ured at an angle of 45 with the plane of the filament, by the factor C 2 . We may calculate, from the fundamental photometric laws, the values of these coefficients C , Ci, and C.,, supposing the form and dimensions of the filament to be accurately known. These values are obtained easily as a particular case of the general problem in which the variations of the intensity with the direction of the ray are determined. To illustrate this let us con- sider the case of an Edison lamp. The quantity of light coming from an element ds, falling on an element ds', equals .dsds* eosOcosB' o = i , r being the distance between the two elements, and & the angles made by r with their normals respectively, and i the luminous intensity of the element ds. The filament of the Edison lamp has the form of an inverted U. Designate by I the length of the vertical branches, by h that of the transverse horizontal branch, and suppose that the filament has a section of rectangular form; designate by a the thickness of this section in the direction of the plane of the filament, and by b the thickness in the perpendicular direction. Let us suppose that the element ds belongs to a sphere con- centric with the lamp and of sufficiently great radius r ; we may then assume that O 1 = 0, and that cos 0' = 1. The quantity of light emitted horizontally in a direction making the angle /3 with the plane of the filament and received by the ele- ment ds' of a very narrow equatorial zone of the concentric sphere jr, equals Iftfj g^asiSL. [2l( a sin + 6 cos/3) + ah sin/3]. 200 PHOTOMETRY. The total quantity of light emitted in the horizontal plane, that is received by a narrow zone of height 8 for which ds' = 8rd(3, is then & = f [2J(d sin/3 + t> cos/3) + ah sin0]d. Integrating, The mean horizontal intensity will then be . Q h _2i T\ J The horizontal intensity of the angle ft is equal to is then true. But the ratio between the mean intensity and the intensity at 45 it still simpler, for we find that it is independent of the dimensions of the filament ; it is, in fact, * = = 0.9003 = ELECTRIC LIGHTS. 201 This result has been confirmed by the direct measurements of Hagenbach and by those at the Munich Exposition, the Vienna Exposition, etc. ; however, the value of the constant determined experimentally is somewhat higher than 0.9003. This is because the section of the filament is not a perfect rectangle as we have supposed; the factor tends then toward unity as the section approaches the form of a circle. By means of eight Edison lamps Hagenbach obtained C = 0.95 ; at Vienna 0.94 was obtained for Maxim lamps, and 0.98 for Edison lamps. In all lamps whose filament has an analogous form to that of the Edison lamp, we may determine the mean horizontal intensity by a single measurement of the horizontal intensity at an angle of 45 with the plane of the filament. We have, then, with satisfactory approximation, . (6) Hagenbach has also given the following formula by which to calculate the mean horizontal intensity : Lo+2L, This formula agrees, in general, very well with the facts. To illustrate, we give the values obtained at Vienna with two Maxim and two Edison lamps, whose difference in the distribution of hori- zontal intensity is very considerable *. Lamp. /AO /A45 /A90 /; Calculated m Observed. Maxim .... 0.999 0.793 0.219 0.701 0.716 Maxim .... 1.021 0.766 0.282 0.709 0.743 Edison .... 1.020 1.029 1.083 1.040 1.046 Edison .... 1.018 1.234 1.224 1.178 1.175 The measurements at Munich, Philadelphia, and Antwerp have also shown the exactness of this formula, at least within the limits of precision of the observations. 127. We may also obtain directly the value of the mean hori- zontal intensity by means of an ingenious method invented by * Experiences faites a V Exposition tf tflectricite de Paris, p. 44. 202 PH O TOMETR Y. Crova*, which greatly simplifies measurements and calculations. The lamp is mounted on clock-work which makes it turn about its geometrical axis four or five times a second ; the current reaches the lamp by two insulated rings on which brushes rest. The lamp appears as an immovable luminous spindle whose intensity is exactly the mean horizontal. It would be preferable to mount the lamp on a small electric motor of high resistance in shunt across the lamp terminals. Then the source which illuminates it would also cause it to rotate. Mean Spherical Intensity. 128. Acquaintance with the form and dimensions of the filament permits the calculation of the distribution of luminous intensity in the various directions ; but this somewhat complicated calculation is of no practical interest. The exact determination of the photometric surface of an incan- descent lamp requires, then, precise measurements. From the fol- lowing considerations it will, however, be seen that they may be considerably abridged. The projection of the filament on a vertical plane varies in a uniform manner when it is turned about its verti- cal axis. From this it follows that the distribution of luminous intensity is similar at all the horizontal parallels of the concentric unit sphere ; that is, the horizontal sections of the photometric sur- face are curves similar to one another and to that of the horizontal intensity. For this reason it is usually sufficient to determine the variations of the luminous intensity with the inclination, in one vertical plane alone ; the variations in the other vertical planes fol- low the same law. [See Appendix E.] It is known that the mean horizontal intensity is equal to C I h0 , I M being the horizontal intensity in the plane of the filament, and C the corresponding reduction factor ; this factor is the same for all parallels of the unit sphere. Now if 1^ designates the mean intensity of the parallel corresponding to an inclination 0, the total quantity of light received by the unit sphere is I em cosO-dO. * Comptes Eendus des Travaux du Conyres des iZlectriciens de 1889 ', p. 208. ELECTRIC LIGHTS. 203 The mean spherical intensity is -*L, or 4?r m = il I em cosO-d9. Now the intensity I em is a function of the inclination of the form, / = j Consequently, If we put we obtain 0-f/7Weosfttf, The constant (7, which is called the factor of reduction of hori- zontal intensity to mean spherical intensity, does not vary sensibly from one lamp to another ; to determine it, it is necessary to have recourse to measurements on lamps of various systems. The mean spherical intensity may finally be calculated by multi- plying the mean horizontal intensity by a factor of reduction C", which may be called the factor of reduction of mean horizontal intensity to mean spherical intensity. We give below the values of the constants C and (7, calculated by means of the measurements made at the Vienna Electrical Expo- sition of 1883. Lamp. Co C Lodyguine 0.998 0.776 Miiller 0.980 0.863 0.981 0.758 Maxim 0.735 0.556 Siemens 1.007 0.748 Bernstein 0.973 0.718 Swan . 1.150 0.946 1.175 0.957 Miiller 1.011 0.875 Lane-Fox 1.006 0.734 204 PHOTOMETRY. Results of the Franklin Institute Tests. 129. Incandescent lamps have been the subject of numerous photometric measurements with the object of determining the dis- tribution of intensity with the direction of the ray. As early as 1881, at the Electrical Exposition, this question was very carefully studied. The measurements of the committees at the Expositions of Munich, Vienna, and Antwerp have also made documents which are very interesting and very useful to consult. But from the point of view of the importance of the tests, it is the measurements of the Committee of the Franklin Institute which excel. Numerous lamps of each type were studied, so that the values obtained for each of them have the significance of mean values, and on this account a greater importance. In tables I. to IV. we have given a r6sum of the principal photo- metric elements of the lamps studied. Table I. contains the principal constants of each type obtained by taking the mean of a large number of lamps (10 or 20). TABLE I. Name and Number of Lamps. Volts. Amperes. Mean Spherical Candle Power. Watts per Spherical Candle Power. Mean Horizontal Intensity. Edison (20) Stanley (10) 97.0 96.4 0.709 551 15.49 13 56 4.48 3 92 18.83 16 54 Woodhouse & Rawson(lO) White (10) . . 55.48 49 99 1.026 1 017 15.09 12 44 3.56 4 08 19.11 15 08 Weston (20) .... 111.4 0.530 16.27 3.63 17.87 Table II. contains the values of the horizontal intensity for different azimuths ; in this table as in the following, the origin of the azimuths coincides with the plane perpendicular to the base of the filament. ELECTRIC LIGHTS. 205 TABLE II. Azimuth. Edison. Stanley. Woodhouse and Rawson. White. Weston. 16.61 16.65 14.71 14.80 19.96 30 18.20 16.60 18.23 14.63 14.99 60 20.45 16.43 20.98 14.97 12.37 90 20.88 16.36 20.42 15.17 16.67 120 20.82 16.35 20.02 15.10 21.51 150 18.86 16.68 18.51 15.13 22.11 180 16.87 17.03 14.48 14.87 19.79 210 18.48 16.85 18.71 14.96 14.58 240 20.74 16.40 21.27 15.00 11.98 270 21.10 16.20 22.46 15.18 16.51 300 20.93 16.43 20.63 15.21 21.74 330 12.12 16.45 18.95 15.08 22.24 In the third table are found the values of the luminous intensity at different inclinations for two azimuths differing by 90. The origin of the inclinations is in the horizontal plane, and they are measured from to 360, passing over the top of the lamp. TABLE III. Edison. Stanley. Woodhouse and Eawson. Weston. 53 1 Azimuth. Azimuth. Azimuth. Azimuth. 5 90 90 90 90 16.70 20.64 16.54 16.23 14.76 20.56 19.82 16.17 30 16.02 18.31 15.29 14.90 13.48 20.00 19.31 15.40 60 9.54 11.93 11.04 11.86 9.60 13.32 16.39 13.74 ' 90 3.57 3.08 6.80 7.00 6.74 5.77 13.39 13.00 120 8.25 11.54 10.35 11.74 10.71 13.17 16.24 13.41 150 14.96 18.21 14.99 14.87 14.06 18.72 19.13 15.63 180 16.82 20.87 16.85 16.81 14.71 21.81 19.76 16.42 210 14.84 17.85 15.00 14.54 14.34 19.62 18.82 15.76 240 9.07 11.11 9.57 9.11 11.28 14.11 16.34 15.08 270 300 9.84 11.68 9.26 10.40 9.75 13.52 17.34 13.83 330 15.06 17.69 14.83 14.33 13.64 18.10 18.78 14.64 206 PHOTOMETRY. Finally, the fourth table contains the constants C , C^ C, and C", which have been calculated from the detailed results published by the Committee of the Franklin Institute. TABLE IV. Lamps. Co c, C a- Edison 1.09 1.26 0.74 80 Stanley Woodhouse & Rawson . "White 1.00 0.88 0.99 0.98 1.23 1.02 0.83 0.74 0.82 0.83 0.83 83 Weston . . . 1.08 0.90 0.98 91 The curves in Figs. 70 to 75 represent the variations of luminous intensity in a horizontal plane, in a vertical plane of azimuth 0, and in a vertical plane of azimuth 90. The first three figures relate to the Edison lamp, the other three to the Weston lamp. FIG. 70. Horizontal Distribution of Luminous Intensity in an Edison Lamp. We have chosen diagrams of these two lamps because of the great difference in the form of their filament. In the first lamp, the filament has the form of an inverted U, while in the second, the ELECTRIC LIGHTS. 207 filament is a helix twisted about a horseshoe-shaped axis. The diagrams show well the influence of these differences in form, especially on the variations of intensity in their vertical planes. FIG. 71. Variations in the Luminous Intensity of an Edison Lamp in the Plane of Azimuth. FIG. T2. Variations in the Luminous Intensity of an Edison Lamp in the Vertical Plane of 90 Azimuth. We have already seen that the horizontal distribution depends on the section of the filament. If it is circular, as in White and 208 PHOTOMETRY. Stanley lamps, the curve of horizontal intensity practically forms a circle. If it is rectangular, as in the Edison, and Woodhouse FIG. T8. Variations in the Horizontal Luminous Intensity of a Weston Lamp. PIG. 74. Variations in the Luminous Intensity of a Weston Lamp in Plane of Azimuth. and Kawson lamps, the maximum horizontal intensity corresponds to the largest side of the rectangle. ELECTRIC LIGHTS. 209 Variations in Luminous Intensity with the Energy expended in the Filament. 130. The luminous intensity of an incandescent lamp varies with the temperature of the filament, i.e. with the electrical energy spent in it. These variations of luminous intensity play an important rdle in the application of incandescent lamps to illumination, for there exists for each lamp a determinate luminous intensity which, corresponds to a given life of the lamp. FIG. 75. Variations in the Luminous Intensity of a Weston Lamp in the Plane of 90 Azimuth. Jamieson * made the first extended systematic researches on the relation which exists between the luminous intensity of an incandes- cent lamp and the energy expended in the filament. He obtained some very interesting diagrams for the ordinary lamps by taking as abscissse the energy expended, and as ordinates the luminous intensity. Dr. Higgs attempted to represent this relation analytically by putting I being the luminous intensity in candles, W the energy expended, and M a constant depending on the nature of the lamp. * Lum. l, Vol. VII. p. 137. 210 PHOTOMETRY. Mansel, at Glasgow, gave also the following equations : log.6 = in which E is the difference of potential at the terminals of the lamp, / the luminous intensity, r the resistance of the lamp, a, 6, and B constants. Jamieson simplified these equations by putting a = 2 A, and by supposing, as is shown by experience to be true, that log bB is a constant ; he then obtained the simpler form, or /= f - t A being a constant. Voit, in his able report upon the electrical measurements of the Exposition at Munich, endeavored to determine a simple analytical law, giving for all incandescent lamps more concordant results than those furnished by the above equations. He investigated the three following equations : and found that the last of these equations represents the observa- tions with sufficient accuracy, save for the Cruto lamps. In 1883, Goetz* of Zurich arrived at the conclusion that the equation I=aW+bW 2 gave more concordant results than any of those previously proposed. However, in 1884, an investigation with the Bernstein lamp made by Ganguillet t, showed that the equation of the third degree, I=aW+(3W 3 , was still more exact. This conclusion was also verified by numerous measurements made by Hess in the electro-technical laboratory at Zurich. * Lum. til, Vol. XI. p. 207. t Lum. l, Vol. XXIII. p. 520. ELECTRIC LIGHTS. 211 In the following table are given the result; obtained with a 16 candle power Swan lamp. The intensity of the current is represented by ; the horizontal luminous intensity measured at an angle of 45 with the plane of the filament is designated by /, while /! represents the luminous intensity calculated by the binomial formula of the third degree, and 2 2 the intensity calculated accord- ing to the cubical formula of Voit. The mean A/j of the deviations / /i and the mean A/ 2 of the deviations / 7 2 , show the relative exactness of the two formulae. E i W I /i /2 33.90 0.90 30.68 1.27 1.00 1.59 40.92 1.10 45.05 4.25 4.51 5.02 44.26 1.18 52.49 7.43 7.67 7.94 45.65 1.22 55.70 9.28 9.26 9.49 48.04 1.29 61.91 13.28 13.26 13.03 49.25 1.32 65.02 13.56 15.54 15.09 /! = - 0.0280 W+ 0.0000632 IF 3 , 7 2 = 0.0000549 TF 3 , A /! = 0.138, A/ 2 = 0.422. Below are the equations for certain lamps, determined from the observations of Hess of the Committee on Experiments at Munich, etc. ; the coefficients are in terms of candles and watts. Lamp. -v- 4T*. '+*.,. Swan No 1 0000974 02778 0i 0.0001164 a u 2 1020 - 0.02434 1196 It It 3 657 - 0.00793 676 11 U 4 549 - 0.0280 632 247 -f 0.0472 215 Siemens 223 - 0.0156 252 Miiller 25 + 0.0391 211 Onto, No. . . u 1 2 . 320 528 + 0.0796 + 0274 196 4910 Edison 22 + 3173 198 212 PHOTOMETRY. These conclusions have been confirmed by later measurements, made in various countries, of lamps of different systems and makes. It may be assumed that the luminous intensity of an incandes- cent lamp is given by the sum of two terms, one of which is proportional to the energy, in watts, consumed in the lamp, and the other to the third power of this energy. This formula applies as well to the luminous intensity of the composite light emitted by the lamp as to that of the principal rays; this follows from the photometric measurements of various physicists, Schumann* among others. Influence of the Degree of Vacuum on the Luminous Intensity. 131. Some exact measurements of the degree of vacuum of common incandescent lamps have been made. It should be remarked at first that the filament has a considerable absorbing property for gases, a property which diminishes at high temperatures ; this then explains the increase in the pressure of the gas in lamps when hot. From a practical point of view, it is the degree of vacuum during incandescence which is of interest. From measurements of Heim f it follows that the pressure in an incandescent lamp when cold is lower than 0.01 mm. of mercury ; when hot, this pressure increases rapidly up to a certain value which does not exceed 0.05 mm., and which remains constant during several hours of burning. There is no advantage in carrying the vacuum too far, to the point, for instance, when there appears about the filament the light blue halo first noticed by Edison ; it has been noticed, in fact, that the filaments of lamps exhausted to this point disintegrate and tarnish the bulb more rapidly. The phenomena of electric evaporation lately studied by Crookes then come into play. From a theoretical point of view, a degree of vacuum as perfect as possible reduces to a minimum the loss of energy produced by the transmission of heat by direct convection of the gaseous particles, a loss which is added to that of radiation. Now, it is known that the luminous intensity varies much more rapidly than the temperature ; thus with an imperfect vacuum, to obtain a determined luminous intensity, it is necessary to expend more energy than with a better vacuum. * Lum. l., Vol. XIII. p. 60. t Lum. l., Vol. XXIII. p. 415. ELECTRIC LIGHTS. 213 The researches of Hess * on the influence of the degree of vacuum in the Swan lamp have proved the accuracy of these conclusions ; it follows from this that the tension of the gas in an incandescent lamp should not exceed 0.2 mm. of mercury to obtain a favorable result. Hess represented by an equation the luminous intensity of a lamp for a given expenditure of energy and for a given tension ; calling Jj the luminous intensity in candles corresponding to an absolute vacuum, 7 2 the luminous intensity for a considerable tension, a a coefficient, the intensity / at the tension p expressed in millimeters is given by the equation For an expenditure of 70 watts, and in a Swan lamp, Hess found J== 4.93 1? + 16.20 j9 2 + 0.96 It follows that 1=16.87 candles if p=0; and 7=4.95 if p = 20 mm. The results of Hess were confirmed by those of Higgins, who investigated three lamps, one of which was filled with air at normal pressure (76 cm. of mercury), the other, half exhausted of air (25 cm. of mercury), and the third having the same vacuum as ordinary lamps. The reciprocal of the efficiency of these three lamps, i.e. the number of watts expended per candle, was found to be 7, 5.3, and 3.5, respectively. It was also determined that the transmission of heat to the surrounding air was in the proportion 32, 25, and 3.5. Variations in the Luminous Intensity with the Life and Rate. 132. As a result of somewhat prolonged use, the filament under- goes quite considerable changes which have an effect on the luminous emission of the lamp. These changes may be summed up as follows : During the first period, somewhat short, the resistance of the filament diminishes rapidly, which has for its effect an increase in brightness. These conditions remain about stationary during a second period, somewhat longer than the first ; they then change, the resistance increases at the same time that the luminous intensity gradually decreases. This phenomenon is produced by modifications in the filament, which becomes little by little wrinkled, while its * Lum. El., Vol. XXIII. p. 523. 214 PHOTOMETRY. section diminishes; it then requires more current to obtain the normal luminous intensity, while the increase in resistance gradually diminishes the intensity of the current. There should also be men- tioned the diminution in the luminous intensity produced by the deposit of carbon which forms on the bulb, and whose thickness increases with the use of the lamp. The most complete measurements of the variations of the photo- metric elements of an incandescent lamp were made at Philadelphia in 1884, under the supervision of the Franklin Institute*. Following are the results of the measurements made on 20 Edison lamps of 16 candle power, at intervals of 100 hours, for a total lighting of 1000 hours. The filament of lamp No. 16 broke after a run of 300 hours, while all the others survived. Some analogous results were furnished by lamps of other makes. Intensity (mean spherical) in Candles. "Wfttts per C&udle. Number of Hours. Beginning. 100 200 400 600 800 1000 Beginning. End. 14.57 1 12.70 12.10 9.20 10.6) 9.83 9.20 4.82 6.97 15.44 14.00 12.50 9.40 11.40 10.80 9.90 4.52 6.65 16.81 15.40 14.40 10.2) 11.30 11.70 9.90 4.24 6.56 16.09 13.60 12.40 9.20 10.70 10.30 9.10 4.24 6.92 15.11 14.30 12.10 9.70 11.70 11.00 9.60 4.55 6.55 14.87 11.00 11.10 9.60 10.60 10.30 9.60 4.58 6.53 15.60 11.50 11.70 10.00 9.60 9.50 7.10 4.43 7.13 15.72 14.10 14.50 9.40 10.90 10.80 9.50 4.37 6.52 16.41 15.10 14.30 9.60 10.90 9.50 10.30 4.27 6.24 15.62 14.30 12.30 9.50 11.30 10.20 9.10 4.:i7 6.92 14.58 13.20 12.10 9.40 11.60 11.00 9.50 4.79 6.55 16.6(5 15.20 13.20 9.60 11.20 10.50 9.50 4.21 6.71 16.02 12.30 10.90 9.10 10.10 10.20 9.60 4.44 6.82 14.38 12.60 11.60 9.50 10.40 10.30 9.60 4.83 6.57 13.76 13.70 12.30 9.00 11.30 10.70 10.00 4.92 6.33 15.65 13.50 12.20 4 40 15.82 12.60 11.10 8.40 9.70 9.50 8.90 4.43 7.14 16.61 14.10 13.90 9.30 10.00 9.80 8.70 4.17 7.15 15.31 13.50 11.90 9.60 10.30 10.10 9.10 4.45 6.81 14.67 14.40 14.00 10.10 11.60 10.60 10.10 4.71 6.27 Mean . 15.43 13.55 12.58 9.50 10.87 10.34 9.38 4.48 6.66 * Lum. til., Vol. XVIII., 1885. ELECTRIC LIGHTS. 215 The diminution in luminous intensity is very sensible; it fre- quently reaches 30 per cent. Greater diminutions are sometimes found. This diminution is also intimately connected with the working of the lamp. In the first incandescent lamps a mean efficiency of -J- candle per watt was assumed, while now this efficiency has a mean value of J candle per watt when the lamp is first lighted. But this increase in efficiency has been obtained at the expense of the life of the lamp, which is as much less as the efficiency is greater. As the luminous intensity varies approximately with the cube of the energy 100 200 300 400 500 600 700 HOURS. FIG. 76. Normal Test of a 16-Candle-Power Lamp. consumed in the filament, it is easy to make a 16-candle-power lamp give 32 candles with an expenditure of about 2 watts per candle, but the lamp will last a much shorter time. In proportion as the luminous intensity diminishes because of prolonged use of the lamp, the resistance of the filament increases and the efficiency rapidly decreases. The curves of Fig. 76 represent the variations of luminous intensity (^4), of watts per candle (B), and of resistance in ohms (7), as functions of the time, these elements being measured every 100 hours. These results were obtained by means of a lamp of 16 candle power (nominal), and the difference of potential was maintained strictly constant at the terminals of the lamp. The results then conform to those obtained in practice. 216 PHOTOMETRY. The diminution in the efficiency of an incandescent lamp with the length of its use is easily explained by means of the physical properties of the filament. The difference of potential E at the terminals of the lamp remaining constant, the intensity i of the current diminishes as the resistance increases ; the energy spent in the filament Ei also diminishes. There results a lowering of the temperature of the filament and, therefore, of the emissive power, since the latter varies about in proportion to the fourth power of the absolute temperature. This fact explains in part the diminution in the efficiency. 3.4 t-3.3 3.2 -115 110 Ohms 235 225 25 50 75 HOURS. FIG. 77. Test of a Lamp whose Luminous Intensity was kept at 16 Candle Power. On the other hand, the resistance of the carbon decreases as the temperature increases. If then the temperature of the filament lowers because of the increase in its resistance, caused by changes in its section, there results a new increase in its resistance and a still more noticeable diminution of the energy expended. These two causes explain the gradual diminution of the lamp's temperature and efficiency. If it is desired to maintain the luminous intensity constant what- ever the length of illumination, it is necessary to gradually increase the difference of potential between the terminals of the lamp in proportion as the resistance of the filament increases; the energy ELECTRIC LIGHTS. 217 expended in the filament then increases with the time ; the life of the lamp is, however, considerably shortened. Curves D, B, C (Fig. 77), represent the variations of the elements of a 16 candle power lamp constantly maintained at this luminous intensity. Curves B and C represent the same things as in the preceding figure, while curve D represents the variations of the difference of potential between the terminals. It is seen that the lamp was not able to stand 100 hours at this rate, the filament failing at the end of about 95 hours. To show how the elements of an incandescent lamp vary when subjected to an abnormal rate, we give in Figs. 78 and 79 the curves 2 4 6 8 10 12 14 HOURS. FIG. 78. Test of a 16-Candle-Power Lamp with an E.M.F. 10 Per Cent too High. of two 16 candle power lamps analogous to those which the two pre- ceding diagrams furnished. The diagrams in Fig. 78 have reference to a 16 candle power lamp subjected to a difference of potential 10 per cent higher than the normal. Those in Fig. 79 have reference to a 16 candle power lamp maintained at the constant luminous intensity of 64 candles. These four diagrams given by Nichols * sum up sufficiently the different phases of the life of an incandescent lamp. * El World, 1890, Vol. XVI. p. 387 ; Lum. l,, Vol. XXXIX. p. 83. 218 PHOTOMETRY. Attention should be called to a fact often kept in the dark when speaking of the efficiency of incandescent lamps. When the merit of a lamp is to be decided, account should be taken of the mean efficiency during the whole life of the lamp, and not merely of its initial efficiency. The latter may be very high for a given lamp, without the mean efficiency being very great, for it frequently hap- pens that the efficiency diminishes very rapidly after a few hours' use. Peirce* investigated 94 lamps of four different makes, designated by the letters A, B, C, D\ those which were furnished by the manu- facturers themselves are marked with a figure 2 ; those which were 20 40 60 80 90 100 120 MINUTES. FIG. 79. Test of a 16-Candle-Po\ver Lamp run at 64 Candle Power. purchased in the market, by the figure 1. The luminous intensity measured was in every case the mean horizontal intensit}^. The curves of Fig. 80 represent the variations in the number of watts per candle required after more or less use ; these curves in general fall a little immediately after lighting, to rise slowly afterwards. The following table contains for each type of lamp, the number * EL World, 1889, Vol. XIII. p. 329 ; Lum. til, Vol. XXXIII. p. 257. ELECTRIC LIGHTS. 219 of watts per candle required, on the average, during the test (850 hours) and the percentage that the mean efficiency is of the initial efficiency (candle power per watt). Lamps. Watts per Candle (mean). Mean Efficiency in Per Cent of Initial Efficiency. Ai 5.25 67% A 2 4.83 64% B 4.58 77% Oi 5.80 60% C 2 5.36 82% Di 4.92 98% Dz 4.92 90% Peirce further came to the following conclusions. The higher the initial efficiency of the lamp is raised, that is, the smaller the initial number of watts per candle, the greater the variations of effi- ciency become. The curve of watts per candle rises quite rapidly, while that of efficiency lowers. If the initial efficiency is small, the variations also are very small. 300 400 600 800 HOURS. FIG. 80. Variation in the Efficiency of Lamps with the Time. There is a striking difference between lamps which at first require from 3.5 to 3.8 watts per candle, and those which require from 4.7 to 5. At the end of the record, the mean efficiency of the 220 PHOTOMETRY. last lamps is superior to that of the first. the following figures are significant : With reference to this Lamps requiring per Candle : Watts per Candle. Mean Efficiency in Per Cent of Initial Efficiency. A 5.59 61 From 3.5 to 3.8 watts, B 5.09 71 C 4.61 82 A 6.07 67 From 3. 8 to 4.1 watts, B C 5.25 4.54 73 86 D 4.57 88 A 5.39 84 From 4.1 to 4.4 watts, B 4.81 87 C 4.79 90 From 4.4 to 4.7 watts, C D 5.60 4.76 82 98 From 4.7 to 6.0 watts, 4.97 101 The Most Economical Life of an Incandescent Lamp. 133. That which is characteristic of the incandescent lamp is that its efficiency is proportionately higher as its luminous intensity is greater. But this increase in efficiency is obtained at the expense of its life. Now, in an electric light plant the running expenses include, aside from general expenses, two items, viz.: 1. The cost of the energy W expended in the filament. 2. The expense of replacing old lamps. When the cost of the energy decreases, the expenditure for replacement increases, and vice versa. There is evidently a deter- minate life of the lamp which corresponds to a minimum total expenditure ; in place of determining the life, we may also calculate the efficiency which makes the total cost a minimum. These calculations are of real interest from the point of view of the economy of a plant; but it is difficult to treat the. subject theo- retically, for the elements of a lamp depend on one another in a way which is too complicated for it to be possible to establish formulae which are simple and really practical. This work has been under- ELECTRIC LIGHTS. 221 taken many times, in different ways and by various men, in particular by Dietrich *, Picou |, Ayrton and Perry t, Desroziers , Grassi ||, and lately by Simon IT. But these theoretical calculations have not, up to the present time, given results which are really useful. To study this question in a practical way, we should start with a type of lamp for which the duration corresponding to various efficiencies is known. We then calculate the total expenditure for energy used and for lamps renewed. By making this calculation for the various values of the efficiency comprised, for instance, between 1.5 and 4.5 watts per candle, we obtain that which gives the greatest economy. This calculation should be repeated for each particular case, for the result depends essentially on the cost of energy. Calculation of the Tint of an Incandescent Lamp. 134. From a study of the incandescent lamp, we may conclude that the filaments of two lamps are at the same temperature when they emit light of the same composition. This conclusion has been confirmed by all the researches, theoretical and experimental, to which the incandescent lamp has been submitted. The composition of the light emitted is shown by the tint j this is somewhat red when the lamp is below its proper candle power ; it becomes whiter as the rate of the lamp becomes more forced. A simple examina- tion of the tint of an incandescent lamp is enough to tell the rate to which it is subjected. The calculation of the tint of an incandescent lamp may be made quite easily by using Crova's photometric method (51), which con- sists, as we know, in comparing the intensities of the luminous radiations in the neighborhood of 0.582 /x. We know that the luminous intensities of two ordinary sources are equal when the intensities of the radiations in the neighborhood of 0.582 /x, are equal. We determine, then, the intensity of the incandescent lamp in terms of the carcel lamp, for the radiations indicated above. The intensity thus v obtained is equal to the total intensity. * Electrotech. Zeitschr., August, 1884. t Bull, de la Soc. int. des EL, Vol. I. p. 315, 1884. t Phil. Mag., Vol. XIX., 1885, p. 304 ; Lum. El., Vol. XVII. pp. 10 and 60. Bull, de la Soc. int. des El., Vol. II., 1885 ; Lum. tfl, Vol. XVIII. p. 603. || Atti del E. Istituto d'incorag. di Napoli, Vol. II., 1889. f filectricien of July 4, 1891. 222 PHOTOMETRY. Next, a second determination T is made for the red rays corre- sponding to 0.657/x; it is sufficient for this to make the observation by means of red glass, chosen with the spectroscope. This glass should transmit rays of wave-lengths included between 0.726/x and 0.589 u.. with a well-defined maximum at 0.657 a. Crova then denned jr the red tint of an incandescent lamp by the ratio Below are the values obtained by Crova* for the tints of various lights : Sun. Voltaic Arc. Drummond Light. Carcel. 0.50 0.59 0.94 and 0.69 1 This is the same thing as saying, that, with the same intensity of light, sunlight contains only one-half as much red light as is contained in the normal carcel light, etc. Using many incandescent lamps nominally of 50 volts, Crova found that, when the rate varied between the extremes of 30 and 90 watts, the red tint varied from 1.33 to 0.88 ; in the first case the lamp is very red, in the second it is overtaxed and of a dazzling white. Comparing different 50-volt lamps, Crova obtained the same tint as that of the carcel, by operating them at a rate varying from 56 to 57.2 watts, according to the lamp. A normal rate which might characterize each lamp would be for instance the rate which gives the lamp the same tint as the carcel lamp or a determined fraction of this tint. The voltage of a lamp might be defined by the number of volts required to give a tint equal to that of a carcel or a determined fraction of this tint. Thus with the tint 1, lamps are too dim ; but they give good light without being overtaxed with the tint 0.9. These considerations would enable makers to furnish lamps of an exactly known voltage. As an example, we may cite three 50-watt lamps, A, B, C, which gave the following results, the watts varying from 30 to 90 : A B C The red tints varied from . The tint is that of the car- cel usin' 1.33 to 0.88 57.2 watts 0.13 to 3.68 carcel 1.18 to 0.79 56.5 watts 0.12 to 3.50 carcel 1.12 to 0.87 56 watts 0.15 to 3.25 carcel The luminous intensities varied from Comptes Penditft du Conyres des Electriciens de 18S9, p. 207. ELECTRIC LIGHTS. 223 Instead of defining the red tint of a light by the ratio , its degree of incandescence might be defined by the ratio inverted, The adoption of this method of measuring the rate of lamps would only necessitate the addition of two glasses or colored baths for which \ = 0.582 p. and X = 0.657 JK. Different Values of the Efficiency of Incandescent Lamps. 135. To complete the study of incandescent lamps, and especially as historical data, we give the principal results relative to the efficiency of the incandescent lamps investigated at the Expositions of Paris and Munich. We might also complete this table by data relative to present lamps ; but these data, taken in great part from the advertisements of makers, have not sufficient scientific value ; besides, they may be found in all the annuals and formularies of the electrician. Further, it should not be forgotten that the initial efficiency of a lamp is far from describing it ; its mean efficiency is more important, and this element is very rarely given. EXPOSITION OF PARIS (1881). Efficiency. Lamps. tensity in Amperes. Volts. Watts. Watts Candles Lamps Candles. per Horse per Horse Power. Power. Edison A, 16 c. p. . 15.38 0.651 89.11 59.11 3.7 196 12.7 Edison A, 32 c. p. . 31.11 0.7585 98.39 76.04 2.4 307 9.9 Swan A 16.61 1.471 47.30 79.59 4.15 178 10.7 Swan B 33.21 1.758 54.21 96.70 2.86 262 8.0 Lane-Fox A . . . 16.36 1.593 43.63 70.89 3.64 173 10.6 Lane-Fox B . . . 32.71 1.815 48.22 89.36 2.76 276 8.5 Maxim A . . . . 15.96 1.380 56.49 79.39 4.09 151 9.5 Maxim B . . . . 31.93 1.578 62.27 10.03 3.07 239 7.5 224 PHOTOMETRY. EXPOSITION OF MUNICH (1882). Efticiency Lamp. AJean In- tensity in Candles. Amperes. Volts. Watts. Watts per Candle. Candles I/orse Power. Lamps per Horse Power. Edison A, No. 1 . . 18.473 0.678 107.6 74.4 4.0 184 10.0 " A, No. 2 . . 21.159 0.809 110.1 90.6 4.2 175 8.2 " B, No. 1 . . 15.576 0.896 59.22 54.1 3.4 216 14.0 Maxim L, No. 1 . . 17.975 1.344 65.14 89.3 4.86 151 8.4 " " No. 2 . . 21.571 1.353 63.0-i 86.7 3.9 188 8.6 Small Swan L, No. 1, 14.909 1.318 39.46 53.0 3.46 212 150 Large Swan L, No. 5, 18.334 1.161 97.65 114.9 6.15 120 6.5 Siemens, No. 1 . . 17.157 0.946 95.60 92.3 5.2 141 8.1 " No. 2 . . 17.170 0.956 100.10 97.6 6.15 120 7.6 No. 3 . . 17.742 0.906 9699 89.6 5.0 147 8.3 Small Miiller, No. 5, 17.661 1.189 70.95 86.0 4.77 154 8.7 " " No. 6, 22.385 1.305 75.29 99.3 4.38 168 7.5 Medium " No. 1, 21.338 1.573 89.16 143.1 6.5 113 5.2 " " No. 2, 24.529 1.423 97.75 141.9 5.67 130 5.3 Large " No. 1, Cruto . . . 32.643 19.687 1.710 3.257 121.20 26.62 281.1 88.4 8.7 4.45 85 165 3.5 8.9 B. ARC-LAMPS. The Voltaic Arc. 136. The voltaic arc is produced by the passage of a current between two carbon electrodes in air raised to a high temperature. The first experiments relative to the voltaic arc were made by Humphry Davy, beginning in 1800*, but those in which this illus- trious English chemist was able to obtain the arc in a continuous manner datj from 1808 and 1809. Davy having taken two small, sharpened rods of carbon, put them in contact, and passed between them the current of a voltaic battery of 2000 elements. On separating the two points a very small distance, he saw produced between them a slightly convex flame, which remained until the distance between the carbons reached 10 cm. The arc disappeared when this distance became greater, and the points rapidly became cold. The carbons when slowly * Lum. El., Vol. IX. p. 248. ELECTRIC LIGHTS. 225 brought toward one another did not give place to any luminous or calorific phenomenon while they were not in contact ; but as soon as they touched, the points became hot, and, at the moment of their separation, the flame burst out instantaneously. Davy gave this arched flame, whose brilliancy was comparable with that of the sun, the name of voltaic arc, which it has kept up to this time. Nature and Appearance of the Voltaic Arc. 137. The voltaic arc results from the incandescence of a jet of particles detached from the electrodes and projected in all direc- tions. This projection, when continuous currents are used, takes place principally from one electrode to the other, and more particu- larly from the positive to the negative. The positive electrode has a very much higher temperature than the other ; while the nega- tive carbon is scarcely a dark red, the positive carbon, at the same ' distance from the arc, is a reddish white over a considerable length. The consumption of the positive electrode for a given time is double that of the negative. It is this difference in the consumption and temperature, observed from the beginning by physicists, which first led them to explain the phenomenon of the luminous arc as a simple transportation of particles from the positive to the negative elec- trode. It is now well demonstrated that although the transference from the positive to the negative electrode predominates in the arc, there exists nevertheless a very active transference from the negative to the positive. The arc resembles, in fact, a trembling flame, whose form is ovoidal between the points of carbon. From time to time a brilliant particle may be seen to leap from one electrode to the other, pro- ducing a luminous flame. On each of the carbons there appear here and there liquid and incandescent globules, due to mineral sub- stances, which become displaced, glide to the point, and leap forth to gain the other electrode. These liquid globules do not appear when the carbons are chemically pure. When the voltaic arc is produced in air, the two carbon rods diminish rapidly in volume because both of them burn ; but in vacuo, this combustion does not take place, and the positive point is seen to become hollow and diminish in weight, while the negative point elongates and increases in volume. The consumption is almost nothing, and only results from particles being projected by the two- carbons outside their reciprocal action. 226 PHOTOMETRY. The voltaic arc is a portion of the electric circuit having all the properties of the other parts of the circuit. The detached particles constitute between the two points a movable chain more or less conductive and more or less heated according to the intensity of the current on the one hand, and the nature and separation of the electrodes on the other. Things go on exactly as if the electrodes were united by a metallic wire or a carbon rod of small section, which amounts to saying that the light produced by the voltaic arc and that obtained by incandescence are due to the same cause, which is the heating of a resisting body interposed in the circuit. Matteucci showed this similarity between the voltaic arc and the other parts of the electric circuit, by slowly separating two iron bars previously- put in contact : a thread of liquid metal appeared at first, became luminous, then broke to give place to the voltaic arc. By examining attentively the voltaic arc produced between two carbon points by continuous currents, we clearly distinguish the arc and the flame. The arc is blue ; it connects the bright parts of the two carbons. The flame is reddish; it envelops the arc and often gives it a violet appearance because of its interposition. This flame sometimes becomes very- long and starts to lick the sides of the positive carbon to a considerable distance; it is changeable and mobile; it contributes to the variations of luminous intensity, and in certain cases disappears completely. It is then especially that the arc appears with the very slightly luminous blue color which is peculiar to it. With currents of from 50 to 70 amperes, the most intense prac- tically in use to supply a single arc, the appearance is modified and presents some peculiarities less known. At first the flame has a purple color around the negative, then, when the carbons are normally shaped, a narrow blue band is dis- tinguished on the bright surface of the positive, and a red halo about the negative ; the intermediate region of the arc is white. Whatever may be at first the form of the carbon rods, they shape themselves in due course ; the positive point takes on the appearance of a truncated cone terminated by a concave surface ; the negative point takes the form of a cone terminated by a blunt point. These forms are more regular when the points are accurately opposite one another and where the carbons are carefully made and free from foreign substances. The arc is produced not only between carbon points, but between all sorts of substances sufficiently conductive. Its brilliancy depends ELECTRIC LIGHTS. 227 on the intensity of the current, the nature of the electrodes, and the medium in which it is produced. With potassium or sodium, for instance, the light is more brilliant than with platinum or gold; there is more light in air than in mercurial vapors. The color of the arc varies with the substance of the electrodes : it is yellow with sodium, white with zinc, green with silver, etc. The appearance of the arc depends also on the form of the electrodes : between a positive point of coke and a negative plate of platinum it presents the form of a cone ; between two carbon points it has the form of an egg or more often that of a truncated cone, etc. 138. The preceding information, taken from Fontaine's treatise on electric lighting, relates to the voltaic arc produced by continuous currents. The conditions of working of the alternate current arc are not the same. In the latter there is no difference between the two carbons which are the seat of similar phenomena. They both become pointed. However, the upper carbon is consumed a little more rapidly than the lower, because of the ascending current of air which tends to consume it at the edge. There results a sensible difference in the distribution of the luminous intensity. The characteristic feature of the alternate current arc is the very disagreeable humming which it produces ; this is very intense and cannot be suppressed. Its intensity may be diminished by sur- rounding the lamp by a closed globe. The cause of this humming is not surely known ; it is thought, however, that it is produced in great part by the rapid extinction and relighting of the arc and by the rapid variations of temperature which result*. The Difference of Potential between the Electrodes of the Voltaic Arc. 139. The voltaic arc is characterized by a considerable fall of potential between the electrodes, a fall which shows that the produc- tion of the arc requires a considerable expenditure of energy. This difference of potential depends on the nature and diameter of the carbons as well as on the length of the arc; it is given, according to Edlund, by the equation Nichols, Electr. World. 1891, Vol. XVII. p. 399. 228 PHOTOMETRY. a and b being constants, and I the length of the arc. Physicists dif- fer greatly as to the significance of the constant a. In the opinion of certain physicists, this constant corresponds to a resistance to passage whose seat is found on the positive elec- trode or in its immediate vicinity ; other physicists, on the contrary, think with Edlund that there is no appreciable resistance to passage, and that the constant a represents an electromotive force opposed in direction to that of the current. [See Appendix F.] Beside these two opinions there should be mentioned other hypotheses, among them that of G. Wiedemanu, who assumes that the voltaic arc is a discontinuous discharge, and that of Lecker, who thinks that the electric current broadens out in passing from one carbon to the other, and is not confined to the neighborhood of their common axis. Among explanations so different it is best to assume that the actions which they contemplate all contribute to the production of the phenomena which accompany the voltaic arc. It seems, however, that resistance to passage plays a princi- pal part in the production of the voltaic arc; at least this fol- lows from precise measurements made by Uppenborn and Lecher in particular. Uppenborn found from many photographs that the voltaic arc has the form of a truncated cone whose very large base rests on the positive carbon, which indicates a very great resistance to pas- sage at this place ; the fall of potential then takes place principally at the passage of the current from the positive carbon into the air. This fact is, moreover, confirmed by direct measurements of potential. With 12 mm. carbons and with lengths of arc varying from 6 to 16 mm., Uppenborn found a mean value for a of 38 volts, formed in part by a fall of potential of 32.5 volts on going from the positive carbon into the air. Lecher proved, moreover, that the potential remains constant in the layer of air included between the two elec- trodes even at a considerable distance from the axis. This discontinuous variation of potential only takes place with carbon electrodes, and is not found with electrodes of iron, platinum, silver, or copper. The constants a and b of Edlund's equation vary with the inten- sity of the current, as well as with the nature and dimensions of the carbons. In this way Nebel found the following values of the difference of potential observed with carbons of different diam- ELECTRIC LIGHTS. 229 eters and with currents of different intensities ; I is millimeters. in Volts with Carbons o f 10 mm. 12 mm. 14 mm. 12 amperes 39.3 + 221 35.2 + 2.6 Z 32.4 + 2.8 Z If) u 39 2 + 2 Z 36 1 + 1.4 I 34.1 + 2.8 Z 20 u 38 + 1 9 Z 34 4 + 2.1 Z 'M u 38 6 + 2 1 Z 34.9 + 1.9 Z FIG. 81. With carbons of different composition, but of the same diameter, using currents of the same intensity (12 amperes), Uppenborn obtained the following values for the difference of potential : Carbon No. 1 . . . . . 35.4 + 2.10 Z " "2 39.0 + 1.74 Z " "3 40.0 + 2.20 Z " "4 41.0 + 2.16 Z " " 6. 45.4 + 1.99 Z Mean 40.1 +'2.24 Z From the figures which precede and from still other results it follows that the difference of potential between the electrodes dimin- ishes as the diameter of the carbons increases, i.e. as their resistance diminishes. This fact is moreover used in low-tension arc-lamps, of which the Weston, much used in the United States, is an example. This dif- 230 PHOTOMETET. ference of potential varies also with the nature of the carbons and may vary by 10 or even 15 volts for carbons of the same diameter but of different sources. The study of the voltaic arc the form and length of the arc, the appearance of the carbons is made very easy by projecting the whole on a white screen by means of a magnifying lens. Figure 81 represents the arrangement of the apparatus with so much precision that it is needless to enter into its details. The Nature and Manufacture of Carbons. 140. The composition of carbons having considerable influence on the photometric properties of the voltaic arc, we give certain details of the manufacture of the pencils employed. It is known that Davy employed pencils of charcoal extinguished in water or mercury ; these burned quite regularly, but too rapidly to be employed commercially. It was Foucault who first replaced the charcoal by the deposits made on the sides of gas retorts. Gas- retort carbon is much denser than charcoal and resists much longer the destructive action of the voltaic arc ; but its composition is not uniform, which produces considerable variation in the luminous inten- sity ; this variation is due to the presence of foreign matter, alkaline salts or earths and silica, which evaporate and help to form the flame which surrounds the arc. Attempts have been made to purify gas- carbon by various processes, but without complete success. The process of manufacture invented by Jacquelaine consists in producing artificially gas carbon free from all impurity by bringing into contact with the incandescent sides of the retort very dense hydrocarbureted material, of which a part volatilizes, and the remain- der decomposes, leaving as a residue a layer of carbon ; by employ- ing well-purified tars, perfectly pure gas carbon is obtained. The carbon pencils of Jacquelaine gave a very white, steady light about 25 per cent more intense than that given by ordinary carbons with equal current. These carbons had the inconvenience of being very hard, which required considerable work in sawing them and occa- sioned considerable waste. The methods used at present for making carbon pencils are due to Carre and Gauduin ; they consist in preparing a suitable paste, triturating and compressing it, then passing it through a die so as to obtain cylindrical pencils which are cut the desired length and baked in a furnace like those used for pottery. ELECTRIC LIGHTS. 231 The composition of the paste varies according to the make. Carre employed at first a mixture of 50 parts very pure powdered coke, 20 parts calcined lampblack, and 30 parts of a syrup made of cane sugar and gum. Pulverized gas carbon mixed with gas tar is now generally used. The quality of the product depends on the pulverizing of the material, and on the baking ; the latter is many times repeated, and between times the carbons are plunged into a boiling concentrated syrup of cane or caramel. In order to maintain the arc at the middle of the carbon, a thing which increases the stability and regularity of the axis, a central hole is made in the carbon, while in the die, and filled with a sub- stance called a core, a little better conductor of electricity than the carbon. The cored carbons give excellent results. They are only employed for the positive pole, because of their relatively high price. In order to prolong the life and increase the conductivity of the carbons, they are often electroplated with copper. Coppered car- bons are very much employed, especially in America. In Europe, bare carbons are more used, because the light is more regular. As to nickeled carbons, they have not yet come into the market. Besides carbons passed through a die, as those of Carre, moulded carbons are also made. In general, carbons made with a die are more dense than those moulded, and are more suitable for low ten- sions, which require a more intense current and should possess greater conductivity. For fuller details concerning the manufacture of arc-light car- bons we refer to special works. Regulators and Candles. 141. The continuity of the voltaic arc is obtained by means of a regulating mechanism which maintains the separation of the carbons at a constant distance for a determined intensity of current and difference of potential. There are a great number of different regu- lators, a great majority of which depend on the following principle: When the length of the arc varies, the intensity of the current varies also, so that the intensity diminishes as the carbons are con- sumed. This diminution of intensity is profitably used to maintain the carbon points at a constant distance, within very narrow limits. For this, there is introduced into the circuit an electro-magnet, whose armature is drawn in one direction by magnetic action and 232 PHOTOMETRY. in the other by a spring. When the intensity of the current dimin- ishes, the magnetic action diminishes, and the armature moves under the preponderating influence of the opposing spring. This move- ment is used to unclamp a mechanism which allows the carbon- holders to approach. In electric candles, the regulation of the voltaic arc is obtained without a regulator. The candles are composed of two parallel rods of carbon with an insulating substance placed between them, and the whole made into one bundle. The carbons burn under the action of the current, and need no mechanism for lighting or regulating them. The length of the arc depends solely on the distance of the pencils, and lighting is brought about by means of conductive priming placed at the top of the points at the time of manufacture. We refer to special treatises for all that concerns the various mechanisms employed in arc-lamps and the study of the best condi- tions of operating them. History of the Photometry of Arc-Lamps. 142. From 1808, when Davy first made the arc-light burst forth, up to the time when the electric light entered into commercial use, the photometric study of arc-lights had scarcely been undertaken. We cannot consider as a complete investigation the researches of Fizeau and Foucault in 1843 and 1844, in the course of which these physicists made a series of comparisons between the chemical action of sunlight, electric light, and oxy-hydrogen light. Although the results obtained have passed into all the treatises on physics, they have only a very restricted value, for they refer to the action of light on a plate of iodide of silver and not to photometric action properly so called. Below are the results : Intensity of sunlight, Apr. 11. 1844, at 11.16 A.M., with a very clear sky . 1000 Intensity of sunlight, Sept. 20, 1843, at 2 P.M., with a pale blue sky . . 751 Intensity of the voltaic arc produced by 3 series of 46 Bunsen elements . 385 Intensity of the oxy-hydrogen light 6.85 The feeble chemical action of the oxy-hydrogen light led Fizeau and Foucault to determine directly by an optical method the photo- metric action of the voltaic arc and the oxy-hydrogen light. The result of this comparison was that the light emitted by the voltaic arc was to the oxy-hydrogen light as 32.6 is to 1.6, while the same ratio determined by chemical action had been found to be as 34.3 is to 1. ELECTRIC LIGHTS. :>33 The similarity of the two results led the two physicists to con- clude that, from a practical point of view, the chemical and photo- genic actions of two luminous sources are equivalent. Passing rapidly over the measurements of Casselmann (1843), which were the first measurements made with the Bunsen photome- ter, over those of Becquerel made on the occasion of the electric lighting tests of Lecassagnac and Thiers at Lyons and in the Place de VEtoile at Paris (1855 to 1857), and over those occasioned by the introduction into light-houses of the electric light produced by means of the Alliance machines, we come to the introduction of the Gramme machine. From this time, the daily increasing development of electric lighting has occasioned a great number of photometric measure- ments. One of the first complete photometric studies of the voltaic arc is that of H. Fontaine, made by means of a Serrin regulator provided with current from a Gramme machine. Mention should also be made of the measurements of Allard and of Sautter and Lemonnier. But photometric measurements have become more numerous and more complete since the time of the Electrical Exposition of 1881, when the more perfect regulation of the machines and lamps, as well as the good quality of the carbons, permitted a more fixed light to be obtained. It is sufficient to mention the photometric tests of the Exposition of Paris (1881), at Munich (1882), at Vienna (1883), at Philadelphia (1884), at Antwerp (1885), etc., to which should be added a number of wholly unofficial tests. Theoretical Examination of the Variations of Luminous Intensity of an Arc-Lamp. 143. From a photometric point of view, that which characterizes the voltaic arc is the great variations in luminous intensity accord- ing to the direction of the ray, variations which are greater than in .any other common source of light. When the voltaic arc is supplied by continuous currents, these variations are greater than when it is supplied by alternate currents. The cause of this difference should be attributed to the preponderating part taken by the positive car- bon in furnishing the light emitted by the continuous-current arc- lamp. The greatest part of the light emitted by the voltaic arc is due to the electrodes which are raised to incandescence. Thus it has 234 PHOTOMETRY. been estimated that in the continuous-current arc-lamp 5 per cent only of the total light emitted is due to the arc, a proportion of 10 per cent is furnished by the negative carbon, and the rest, or 85 per cent, by the positive carbon. The intensity of the lamp is then the resultant of the intensities produced by the arc and the carbons. Now the quality of the light emitted by an incandescent body is proportional to the emissive power of the latter ; a quality of carbon should then be employed whose emissive power at high temperatures is as great as possible. We know that the emissive power of carbon is very great, greater for instance than that of the majority of metals : it is this that explains the particular brilliancy of the arc obtained with carbon electrodes. In the continuous-current arc, the greater part of the light emitted comes from the end of the positive carbon, which is generally placed above the neg- ative so that the rays may be thrown upon objects below which it is desired to illumi- nate. A simple examination of the calorific conditions of the arc permits one to deduce with sufficient exactness the variations in luminous inten- sity with the direction of the rays. Suppose that the carbons terminate theoretically in two- equal truncated cones ; the arc bursts forth between their ends ; the crater which is formed at the extremity of the positive carbon emits the greater quantity of light, for the emissive surface is greatest there and the temperature highest. It is practically only the arc and the sides of the carbons near their ends which emit light horizontally. Further, the shadows thr,own by the positive and negative carbons limit the emission of light more rapidly as the arc becomes shorter ; the opening of the luminous cone is greater as the arc is longer. But as the length of the arc increases, the temperature of the carbons falls, and the intensity of the light emitted diminishes. 800 FIG. 82. Variation in the Intensity of an Arc- Light with the Inclination. ELECTRIC LIGHTS. 235 This summary examination shows, then, that the luminous inten- sity must be zero in a vertical direction, must pass through a maxi- mum in a particular direction below the horizontal, and through a minimum in the horizontal, to increase and also decrease rapidly above the horizontal. This last conclusion alone was not entirely confirmed by the photometric observations because of various things which modify the regularity of the radiation of light from the nega- tive carbon, and principally because of the fact that the light emitted by the arc in a horizontal direction is more intense than that which the negative carbon emits upward. Thus the minimum in the hor- izontal plane does not always exist, and the diminution continues regularly above it. The diagram which represents the variations in luminous in- tensity with the inclination of the rays is well known; that in Fig. 82 gives the result of all the photometric measurements made on arc-lamps at the Antwerp Exposition. Variations of the Luminous Intensity with the Azimuth. 144. Since everything in the voltaic arc is in general symmet- rical with reference to the axis of the carbons, the luminous intensity should be independent of the azimuth of the ray; i.e. the photometric surface should be a surface of revolution. This would be so, in fact, if the carbons were homogeneous and well centered and if the regu- lator always performed its functions. Unfortunately these condi- tions are not always fulfilled, so that it is not exact to assume that the intensity is independent of the azimuth, although this hypothe- sis is generally accepted in practice. Centering the carbons, in par- ticular, offers the greatest difficulty ; whatever be the care with which the carbons are made, they always undergo a slight bending after burning some moments, which produces a lateral displacement of the points and a disturbance in the distribution of the luminous intensity. This disturbance is much more sensible than is generally sup- posed. It has been noticed by all who have made photometric measurements of the arc-lamp. It has been recently studied with care by Wedding*. This engineer measured the luminous intensi- ties for various inclinations in two azimuths differing by 180. He used in all nine pairs of carbons, working regularly with a current of 14 amperes. He further photographed the carbon points in the course of each of these tests to determine the cause of the irregularities. * Elektr. Zeitschrift, 1889, p. 337. 236 PHOTOMETRY. The following table contains the measurements of Wedding ; they confirm a conclusion arrived at from the measurements at Paris and Antwerp, namely, that the variations of the maximum luminous intensity are much less than those of the horizontal intensity. In this table the luminous intensities are expressed in candles. Carbons. Horizontal Intensity. Maximum Intensity in Candles. Mean Spherical Intensity. Left. Kight. Left. o Right. e 1 109 13t5 1720 43 1860 40 1246 2 147 350 2000 43 2110 39 1246 3 121 157 1790 46 1890 42 1114 4 152 199 1670 42 2310 46 1260 5 155 228 2050 45 2500 41 1355 6 124 373 1860 42 2180 41 1239 7 143 408 2020 42 2480 38 1359 8 183 224 2010 43 2990 43 1179 9 136 171 1710 44 2000 43 1056 Mean . . 141 250 1870 43 2158 41 1228 The curves which represent the detailed results of these measure- ments show that the real distribution of the luminous intensity of the voltaic arc is most irregular ; the photometric surface is far from being a surface of revolution. In calculations based on the luminous intensities of electric lights, one must be content with a rough approximation. Variations of the Luminous Intensity -with the Inclination. 145. This photometric element of arc-lamps is the best known ; the curve which represents these variations differs relatively very little from lamp to lamp. "Wybauw has combined all the photometric measurements of arc- lamps made at the Antwerp Exposition in 1885, and has obtained from them a mean curve representing the variations of luminous intensity with the inclination ; this diagram is reproduced in Fig. 82. The curve obtained * is much like an ellipse whose axis is the radius vector at 40 ; it decreases about symmetrically above and See Appendix G. ELECTRIC LIGHTS. 237 below, but this decrease is very small in the neighborhood of 40. The mean values deduced from 26 lamps differing in their construc- tion arid rate, deviate very little from the particular values of each lamp, the mean intensity being represented by 1000. The following table gives the values of the intensity for the in- clinations included between 60 above and 70 below the horizontal : Luminous Intensity. Observed. Calculated. 60 Above the horizontal .... 48 28 30 " " " .... 110 104 208 208 10 Below the horizontal .... 401 421 20 *i .... 612 629 30 *' " " 871 824 40 " " " .... 1000 1000 50 "" " .... 807 800 60 .... 457 457 70 4t 4i 4 .... 188 206 146. These results have been confirmed by all measurements since those at Antwerp. An exhaustive study of them permits the following conclusions to be made : In the majority of continuous-current arc-lamps, we may distin- guish on the unit sphere four well-defined zones relating to the distribution of luminous intensity about the light-center. In the upper hemisphere, which receives only a small part of the total light, the luminous intensity varies about proportionally to sin 6 ; it may then be represented by i'=H(l-smO), H being the horizontal intensity and being reckoned positive above the horizontal. In the lower hemisphere, there is distinguished: first, a zone (between and 40) in which the luminous intensity is of the form i" = H + asiuO, being counted positive here also ; then a zone more or less narrow (between 40 and 45), in which the variations of luminous intensity are very slight, for which OF THE triI7ISlT7 238 PHOTOMETRY. M being the maximum intensity ; the width of this zone depends on the nature of the crater of the positive carbon ; finally a zone in which the intensity decreases according to the law The luminous intensity / is then represented by the complex formula sintf)]? + [H + osin0]6 + [Jf]g + [b - using that part only whose limits include the inclination for which the luminous intensity is to be calculated. When the variations of luminous intensity are sensibly the same above and below the maximum, at least in its immediate vicinity, the constant term may be suppressed, which is the same as suppos- ing 6 l = 6 2 - We then have The constants a, 6, c may easily be expressed in terms of H, M, OH and 2 - For = 0i we should have /= M; whence, M = H + a sin $ M-H or a Similarly, we may find M 1 sin 2 The complete equation then becomes No considerable error is made by assuming in practice that the luminous intensity is a maximum, and sensibly constant between 40 and 45 ; the equation may then be written + [3.413 Jf(l -sin ELECTRIC LIGHTS. 289 By substituting for H and M the mean values deduced from the Antwerp experiments, we obtain 1= 208 [1 - sin0]8 8 + [208 + 1232 sin0]$ 3 + [1000]$ +3413 [1- sin 0]g. By means of this equation, the values included in the third column of the preceding table (p. 237) were calculated. Consulting the table, we find the agreement as great as possible. By means of an analogous equation the luminous intensity of arc- lamps of any system may be represented with sufficient exactness provided that continuous currents are used. It should always be remembered that individual results may show considerable differences if the measurements are limited to a single azimuth ; to obtain sufficient agreement, the measurements should be made in at least four different azimuths, so as to eliminate irregular- ities in the working of the lamp or in the consumption of the carbons. Rousseau, moreover, dwells on this point with considerable force in his report on the Antwerp tests, and the measurements of Wedding, mentioned above, confirm this conclusion. Mean Spherical Intensity. 147. In what precedes no attention has been paid to mean spher- ical intensity. Up to the present too great value has been given to this element, which only plays a very small part in problems of illu- mination by bare arc-lamps. The most important element in the arc-lamp is the maximum intensity; a knowledge of the horizontal and maximum intensities easily permits the calculation of the intensity for a given inclination, and it is the latter which should be employed in calculating the illu- mination at a given point. The mean spherical intensity should not be employed in calculating illumination, instead of the effective intensity for the inclination considered. The mean spherical intensity gives a basis for calculating the coefficient of transformation of the lamp, or its efficiency if desired, but that is all. Of two lights of the same mean spherical intensity, that will be the better which has the higher maximum intensity, since it is this maximum which determines the limit of the lighting power of the lamp, the illumination always being sufficient below the lamp, especially if a reflector is employed. However, it is sometimes of interest to know the mean spherical intensity of a given lamp, especially as this quantity is easy to cal- culate by an approximate formula which is precise enough. 240 PHOTOMETRY. The exact calculation of the mean spherical intensity is very laborious, since it requires precise measurements at a great number of inclinations close together. However, if we designate by H the horizontal intensity and by M the maximum intensity, we may repre- sent the mean spherical intensity S by the equation already proposed at the Electrical Exposition at Paris in 1881 : The following table made from the official report of Rousseau represents the result of the Antwerp photometric tests on lamps of various systems with carbons of different kinds (Siemens, Schmel- zer, etc.). Intensity (in Carcels). Deviations in Per Cent 0-C. Horizontal. Maximum. Mean Spherical. Observed. Calculated. - 102 557 522 471 446 373 362 423 265 265 276 185 190 120 209 206 177 207 100 94 72 102 145 52 60.6 198 192 166 161.5 132 120 137 119 96 100 68 66 43 70 59 68 61 35 31.5 28 35 48 18 16.3 188 182 154 158 123 121 142 114 93 97 75 66 43 73 68 58 74 35 32 27.5 41.5 47 18 19.8 + 5 + 5 -f 7 + 2 + 7 - 1 - 4 + 4 + 3 + 3 -10 - 4 -15 -21 - 2 + 2 -12 -f 2 -21 2 Brush 102 72.5 92 60 61 73 95.5 54 56 57 36 25 42 34 26.5 44.5 21 17 19 32 22 10 9.4 3 Gramme 4. Piette and Krizik . . 5. Crompton .... 6. De Puydt .... 7 Dulait 8 Gramme 9 " 1 10. Piette and Krizik . . ' 11. Cramer and Dornfelt . ' 12. Piette and Krizik . . , 13 Pieper 14. Brush 15. Piette and Krizik . . 16. " " " . . 17. Gulcher 18 Pieper . . 19 " .... 20. " 21 Brush 22 Gramme .... 23. Pieper 24 " ELECTRIC LIGHTS. 241 The last column of this table gives the percentage deviation between the results furnished by direct observation and those calculated by means of the preceding equation. The mean of the deviations is 5.7 per cent ; that of the positive deviations (9 in number), 5.2 per cent; and that of the negative deviations (10 in number), 9 per cent. Uppenborn also applied this rule to the photometric measure- ments made on seven different lamps ; the results of this comparison are given in the table below. LAMPS. Authority : Uppenborn. CANDLE POWER. Deviation in Per Cent 0-C. Horizontal. Maximum. Mean Spherical. Observed. Calculated. 1 250 1464 470 491 - 4 2 456 3250 1145 1040 + 9 3 560 3071 1221 1048 + 14 4 744 1227 692 679 + 2 5 122 840 274 271 + 1 6 586 2100 802 818 - 2 7 935 1150 767 755 + 2 Finally, Marks also made use of this formula to discuss his own measurements ; he further took a certain number of different observer tions made in America by many electricians. All these results of such varied origin are included in the following table (p. 242) ; they agree almost perfectly with the equation. The agreement between observation and calculation is close enough, although somewhat less so than in the preceding measure- ments; the mean of the deviations is 9 per cent in place of 5.7 per cent. All these results then give to the equation ' H.M = + a really practical value ; it may be applied in all cases with surety greater in proportion as the values of H and M have been deduced from measurements made in several azimuths. This equation might also be simplified by noticing that, accord- ing to Kousseau's measurements with respect to 24 different lamps, 242 PHOTOMETRY. LAMPS. Authority : Marks. CANDLE POWER. Deviation in Per Cent O-C. Horizontal. Maximum. Mean Spherical. Observed. Calculated. Western 344 299 576 313 233 180 389 451 609 576 1235 1395 534 617 1380 1377 348 295 640 609 240 263 653 574 324 293 597 504 249 244 539 569 + 7 + 1 -f 7 + 17 4 + 7 + 17 + 1 n it Brush Ball Brush (1200 c. p.) . . . Brush (2000 c. p.) . . . Van De Poele .... ". " ** .... 333 1155 470 455 . + 3 Weston Electric . . . 263 355 186 220 -18 Thomson-Houston . . . 227 1080 425 383 + 10 tt (t 222 626 288 267 + 7 14 i( Weston 382 594 475 1131 1183 871 525 514 400 474 593 436 + 9 -16 - 9 u the horizontal intensity is equal to 0.208 of the maximum intensity ; we have then approximately H = 0.2 M, whence S = 0.35 M. However, this equation is not absolutely reliable, for the hori- zontal intensity is an element which varies considerably from lamp to lamp ; it would be better to keep to the complete formula. The Employment of Opal Globes and Reflectors. 148. Bare arc-lamps are quite rarely employed, for the light emitted is too harsh in the neighborhood of the lamp, and the total effect of illumination is less advantageous. Bare lamps are employed in the illumination of work-yards and large open spaces. In street lighting, the use of opalescent globes has prevailed, although they absorb a quite large proportion of the light, estimated by von Hefner- Alteneck * at *Lum.tfL, Vol. X. p. 498. ELECTEIC LIGHTS. 243 15 per cent for alabaster glass, 20 per cent for opal glass, 30 to 60 per cent for milky glass. These globes are almost always surmounted by reflectors planned to throw the light from the upper hemisphere down toward the ground. The presence of the globe and the reflector modifies totally the distribution of the light. Uppenborn found that spherical globes give better results, from a photometric point of view, than elliptical ones. There is less absorption, and the distribution is more advantageous. The opalescent globe which surrounds the arc does not absorb the light uniformly ; the luminous intensity of the parts of the globe which correspond to the maximum intensity is sensibly decreased, while that part which corresponds to the minimum is increased. The globe itself becomes luminous and plays the part of a radiant. The nature of the globe, its dimensions, and its form are not without importance. It is generally assumed that the globe should be small, like that of the Cance lamp for instance, so as to replace the point which is too brilliant for the eyes and casts too dense shadows, by a disc whose brightness seems about uniform and which appears as the sun, subtending a small angle. If too large a globe is taken, this effect is completely wanting. In the middle is seen a brilliant point, then the surface of the globe whose brightness is divided into more or less luminous zones. The glass of which the globe is made should be opaque enough to obtain sufficient diffusion, while absorbing as little light as possible. This result is obtained by taking an uncolored glass, having on one of its faces a very thin layer of milky glass sufficiently transparent so that in the daytime, when the lamp is extinguished, the form of the carbons may be clearly distinguished through the globe. With this glass as good results are obtained as with the Cance globes, which are very thick, and much less light is lost. The most exact data which we possess concerning the employ- ment of globes and reflectors with arc-lamps, are those obtained by Wedding* in the course of an examination of the arc lighting of the streets of Berlin. The addition of different globes (I, II, III) to the 14-ampere arc- lamps mentioned in 144 gave the following results : *Elektr. Zeitschrift, 1889, p. 338. 244 PHOTOMETRY. Number of Globe. Horizontal Intensity. Maximum Intensity. Inclination of Maximum. Mean Hemispherical Intensity. Weakening in Per Cent. I 419 970 35 710 41 II 519 1093 37 111 40 III 497 715 35 590 53 The curve which represents the variations of luminous intensity of the lamp with a globe and a polished tin reflector has the same form as the curve of the bare lamp. The dimensions are slightly larger than those above, which naturally corresponds to an increise in the mean hemispherical intensity. In fact, there was obtained with the reflector and globe II : Horizontal Intensity 548 Maximum Intensity (at 38) .... 1207 Mean Hemispherical Intensity . . . 865 The mean hemispherical intensity without either globe or reflector was 1278. Consequently the diminution was 32 per cent in place of the 40 per cent found without the reflector. The employment of the opalescent globe and the reflector prevents taking into the calculation the real intensity instead of the mean hemispherical intensity, for it is not possible to express the lumi- nous intensity simply in terms of the inclination. In this case everything points to taking the mean hemispherical intensity of the lower hemisphere and treating the light as uniform. Variations of the Luminous Intensity with the Intensity of the Current. 149. To establish a relation between the luminous intensity of an arc-lamp and the energy expended in the lamp it is necessary to consider that photometric element of the lamp which is the most constant, namely, the maximum luminous intensity. The most varied photometric measurements have, in fact, always proved that the maximum luminous intensity is least liable to the sudden variations which are, on the contrary, so noticeable in the horizontal intensity. The energy expended in the lamp may be divided into two parts, viz. that which is employed in regulating the lamp, and that which supports the voltaic arc ; it is known that the loss of potential due to the regulation of the lamp amounts, on the average, to 15 volts in ELECTRIC LIGHTS. 245 60, or 25 per cent. A lamp gets from 60 to 65 volts, while the arc itself gets only from 45 to 50. From the point of view of luminous intensity, it is only the part of the energy expended in the arc which should be taken into account : calling V the difference of potential between the two carbons of the lamp and i the intensity of the cur- rent, the energy expended in the voltaic arc is equal to Vi. The problem consists then in finding a relation between the maximum luminous intensity I m and the work Vi. It may, however, be simplified. In practice, lamps always work with a difference of potential which is sensibly constant, even when the regulating is done by constant current. The great majority of lamps use a difference of potential of from 45 to 50 volts. There are, however, lamps which use from 37 to 40 volts, and others, called low tension, for which a difference of potential of about 30 volts is sufficient. We may then assume a constant value for V, so that the problem is reduced simply to finding a relation between the maximum luminous intensity I m and the current i. But for this, it is neces- sary to determine the constants of this relation for each particular group ; we may distinguish three principal groups in which we shall classify arc-lamps : high-tension lamps (50 volts on the average), medium-tension lamps (40 volts), and low-tension lamps (30 to 35 volts). Even a summary examination of the results of the principal pho- tometric measurements to which arc-lamps have been submitted permits the conclusion that the establishment of an equation of out- put is very difficult, because of the influence on the luminous inten- sity of the particular qualities of each lamp, and because of the nature of the carbons ; further, account should be taken of the fact that the photometric unit in terms of which the results are given is frequently badly defined; it is said simply that the luminous intensity is expressed in candles, without indicating either the kind of candle used or the conditions under which it is employed ; now there are differences between the values of different candles which may reach 20 per cent. Hence a new source of difficulty arises in establishing an equation giving even an approximate relation between the lumi- nous intensity and the intensity of the current. We shall only mention, in order to call attention to them, two empirical rules given about 1880 by Maxim and Gravier for calculat- ing the luminous intensity of the arc by measuring simply the surface of the crater of the positive carbon or the hourly consumption of carbon. According to Maxim, to obtain the luminous intensity in 246 PHOTOMETRY. candles, it is sufficient to multiply the surface of the crater, expressed in hundredths of an inch and squared, by the coefficient 10. Gravier calculated in carcels the horizontal luminous intensity of an arc-lamp by multiplying the volume of carbon consumed per hour by a coef- licient which is the same for carbons of the same quality. It is needless to say that these two methods have no practical or scien- tific value. Tischendoerfer* has given a formula which, according to him, represents exactly the variations of luminous intensity of an arc- lamp with the intensity of the current. In this formula, although the author does not expressly say so, he deals with the maximum intensity expressed in candles, the intensity of current being expressed in amperes. This formula is the author does not say on what measurements he has based his calculation, nor between what limits it is valuable. At first sight, it may be said that this formula represents with sufficient exactness the values given by direct observation, since it includes two arbitrary constants and three independent terms. But as the author has not said on what measurements he has based his calculations or whether this formula is a simple empirical rule, it should be compared with direct observation before forming a definite opinion of its value ; this has been done in the table on page 249. 150. We have made a formula of photometric output deduced from experiment alone f. For this we have chosen the most precise photometric observations, made under the same conditions and using the same photometric standard in order to avoid as far as possible errors due to reductions to the same unit, and personal errors. Now, in our opinion, the observations made by Rousseau at the Antwerp Exposition best fulfill the preceding conditions. These observations are twenty-four in number, no account being taken of some which are more or less uncertain ; the intensity of the current varied between 4 and 20.7 amperes, the maximum luminous intensity between 52 and 557 carcels. The observations are repro- duced in the following table ; the order of lamps is the same as in the table on page 240. *Elektr. Zeitschrift, 1890, p. 304. t Lum. El., Vol. XXXVII. p. 408. ELECTRIC LIGHTS. 24' Lamp. Intensity of Current, Y. Differences of Potential, Maximum Luminous Intensity Im (Carcels). Deviations 0-C. Watts per Spherical Carcel. 4.96 Observed. Calculated. 1 20.7 47.5 557 583 -26 2 19.0 50.6 522 519 + 3 5.00 3 15.9 46.2 471 417 + 54 4.43 4 15.6 46.4 446 407 + 39 4.48 5 14.9 47.7 373 386 - 13 5.38 6 14.8 44.9 362 382 -20 5.53 7 14.6 47.0 423 376 + 47 5.00 8 12.9 45.5 265 325 -60 4.92 9 12.5 47.3 265 313 -48 6.13 10 10.8 45.5 276 265 + 11 4.91 11 8.6 47.6 185 205 -20 5.99 12 8.2 47.5 190 195 5 5.93 13 8.0 38.5 120 . 7.22 14 8.0 ' 46.3 209 190 + 19 5.28 15 7.9 48.0 206 187 + H 5.43 16 7.6 44.9 177 179 - '2 5.91 17 7.6 46.0 207 179 + 28 5.78 18 7.0 38.4 100 7.70 19 6.1 38.2 94 7.37 20 6.0 38.5 72 . . . 8.11 21 6.0 47.1 102 140 -38 8.12 22 5.6 46.2 145 130 + 15 5.38 23 4.2 37.0 52 8.66 24 4.0 38.4 60 9.45 The Pieper lamps require a difference of potential of from 35 to 40 volts only, while others require from 40 to 50 volts ; the results which the former furnish should be excluded, since these are lamps of mean tension, while the others are of high tension. We have put x, y, z being coefficients to be so determined that the above equation may represent as faithfully as possible the experimental results. Each observation furnishes one equation; we thus obtain as many equations as observations, viz. eighteen. Applying the method of least squares to this set of equations, we obtain = 0.3815, = 19.666, 248 PHOTOMETRY. and for the equation desired, I m = 7.93 +19.666 i + 0.38151 2 . (I.) By this equation the maximum luminous intensity I m was calcu- lated for each of the eighteen observations of the table, and the values in the fifth column were obtained. The numbers in the next to the last column are resulting errors, i.e. the deviation between the calculated and the observed values. In the last column we have written the values of the mechanical equivalent of the carcel for each lamp. Therefore the above equation represents as faithfully as possible the variations of luminous intensity with intensity of current, at least as found at Antwerp. Attention should be called to the fact that these experiments were made on lamps of different systems, using carbons of different natures ; from this then results a much greater generality for the equation, although the residual errors would have been much less had the work been done on lamps of the same make, employing carbons of the same kind. The equation applies to arc-lamps under normal conditions having a difference of potential of about 48 volts ; it may be applied to intensities of current varying from 4 to 30 amperes, although the measurements on which it depends were not carried above 20.7 amperes ; we may, nevertheless, assume without difficulty this extra- polation. We have simplified equation (I.) so as to give it a practical value by putting (II.) The loss of the constant term is compensated by the increase of the coefficient of the term of the second degree. The agreement of the results of the simplified formula with those of the original formula is as close as could be desired. In the following table will be found the values obtained by means of the two formulae for different values of the intensity of the current. ELECTRIC LIGHTS. 249 VALUE or I m (IN CARCELS) ACCORDING TO FORMULA. i I II Of Tischendoerfer. 4 amperes 92.7 86 37 6 " 139.6 134 78 8 " 190.0 186 125 10 242.7 240 178 12 " 298.8 298 237 14 358.0 358 303 16 " 420.2 422 376 18 ^ 484.5 490 453 20 553.8 560 537 30 " 941.2 960 603 To compare the values given by Tischendoerfer's formula with those given by formulae (I.) and (II.) it is necessary to transform candles into carcels ; assuming that Tischendoerfer had in view the German candle, which is approximately \ carcel, we obtain the values in the last column of the table. It is seen that this formula gives results which are too small for small intensities of current. The formula which we have obtained makes no pretension to being perfectly exact ; it is simply an approximate formula allowing the deduction, within 10 or 20 per cent, of the luminous intensity of a normally working arc-lamp, by the simple reading of an ampere- meter. This exactness is quite sufficient for arc-lamps, where the varia- tions are frequently so great. We have seen above that it may be assumed without harm that the horizontal intensity is equal to one-fifth of the maximum. The formula in 146 then permits the intensity to be calculated for a given inclination, so that the photometric problem of arc-lamps may be completely solved by a simple galvanometer-reading. In recent years, the habit has grown more and more of designating arc-lamps not by their luminous intensity, but by the intensity of the current. This use has spread because of the considerable differ- ence which generally exists between the nominal intensity and the real intensity. The preceding formula may give some useful infor- mation on the maximum luminous intensity of these lamps, and by taking account of the relation S m = 0.35/ m , on the mean spherical intensity. 250 PHOTOMETRY. 151. Of the value of the mechanical equivalent of the unit of light obtained with continuous current arc-lamps, equation (II.) permits an exact enough determination in terms of the current; we obtain, in fact, S m = 0.35/ TO = 0.35 (20 i + 0.4 i) . The energy expended is equal to W= Vi ; the mechanical equiv- alent of the carcel is then equal to the quotient of W divided by S m -, i.e. Vi V i* 7-H0.14t' But V is equal to about 50 volts ; we have then 50 7 + 0.14;' This formula gives the following values for : i = 4 amperes 6 10 15 20 30 6.61 watts 6.38 5.95 5.49 5.10 4.46 Below are the values given by Fontaine for constant current regulating arc-lamps : Amperes. Mean Luminous Intensity. Mechanical Equivalent. Carcels. Candles. Watts per Carcel. Watts per Candle. 50 600 4980 4.8 0.60 30 525 3500 5.7 0.72 20 240 1990 6.0 0.75 14 175 1450 6.2 0.78 10 100 830 6.5 0.82 8 75 620 7.2 0.90 6 50 410 8.0 1.00 4 26 210 9.0 1.13 [The relation between carcels and candles is not exactly the same in columns 4 and 5 (8 : 1), as in columns 2 and 3 (8.3 : 1). Trans.'] ELECTRIC LIGHTS. 251 Alternate-Current Arc-Lamps. 152. The preceding results cannot be applied to alternate-current arc-lamps, for the law of variation of luminous intensity with incli- nation of the rays is completely different. A simple examination of the physical state of alternate-cur- rent carbons shows the reason for this. In continuous - current arc-lamps there is a fundamental difference be- tween the positive and negative car- bons, the former emitting much more light than the latter. In the alter- nate-current arc, this difference does not exist, and the two carbons have absolutely the same appearance, so that the emission of light from the upper carbon is the same as that from the lower. The distribution of luminous intensity should be symmet- rical with respect to the horizontal plane passing through the arc ; more- over, measurements have shown this. Further, in a horizontal direction it is the arc especially which emits the greatest quantity of light, the two carbons emitting their light in an oblique direction. Now we know that the luminous power of the arc itself is relatively low ; it follows then that the luminous intensity should have its minimum value in the horizontal direction. The measurements of Fontaine, made at the introduction of the Gramme lamps, had given a result contrary to the preceding conclu- sions in this particular, that the horizontal luminous intensity had a value about equal to the maximum value. This result was accepted for a long time, although contrary to the conclusion arrived at from a theoretical examination of the light emitted by the lamp. Some recent measurements by Uppenborn, made with great pains with eight different carbons, gave for the meridianal curve of the photo- FIG. 83. 252 PHOTOMETRY. metric surface some quite regular curves, but agreeing with the pre- ceding conclusions. The three curves of Fig. 83 relate to three different lengths of arc, 2, 3, and 4 mm., obtained with a constant intensity of current of 8 amperes, and with the same carbon ; the curve with a continuous line was obtained from a length of arc of 2 mm.; that with dotted lines from a length of 3 mm., and that with alternate dots and lines from a length of 4 mm. From these diagrams the conclusion follows that the distribu- tion of light is not entirely symmetrical with respect to the horizon- tal plane, and that the minimum is produced in a direction differing slightly from the horizontal. To complete these results, we give the values of the mean spher- ical intensity obtained with three sorts of carbons (S, M, K) for lengths of arc of 2, 3, and 4 mm. 2 mm. 3 mm. 4 mm. S 180 188 331 M 210 265 264 K 292 290 280 These figures show then that the most favorable length of arc may vary considerably with the kind of carbon employed. Below are some data, according to Fontaine, relating to alternate- current arc-lamps. ALTERNATE-CURRENT ARC-LAMPS. Intensity of the Current in Amperes. Mean Luminous Intensity. Mechanical Equivalent. Carcels. Candles. Watts per Carcel. Watts per Candle. 35 175 1450 9.0 1.13 20 110 910 10.8 1.35 12 46 380 14.4 1.80 153. The distribution of luminous intensity of arc-candles, inter alias Jablochkoff candles, differs sensibly from that of lamps in which the carbons are situated in the same axis. The two pencils being placed side by side, the intensity varies greatly with the azi- muth, no account being taken of variations with the inclination. ELECTRIC LIGHTS. 253 The horizontal intensity is maximum in the direction normal to the plane of the candles, and minimum in this plane. The curve which gives the distribution of luminous intensity in the horizontal plane has the form of a lemniscate whose minor axis corresponds to the plane of the pencils and whose major axis is perpendicular to the same. The efficiency of the candles is somewhat less than that of regu- lating arc-lamps, as the following table shows : Intensity of Current in Amperes. Mean Luminous Intensity. Mechanical Equivalent. Carcels. Candles. Watts per Carcel. Watts per Candle. 10 62 510 14.5 1.81 8 45 370 17.6 2.20 6 32 260 19.6 2.44 5 24 200 22.4 2.80 3 10 63 28.8 3.60 C. MISCELLANEOUS INFORMATION CONCERNING THE USUAL SOURCES OF LIGHT. Rate of Consumption of the Principal Sources of Light. 154. In the chapter devoted to photometric standards certain information was given as to the luminous intensity and consumption of the common sources of light. This information is sufficient for candles and oil lamps. It is well to complete it for the various systems of gas-burners and for the most common petroleum lamps. Of magnesium lamps, which give a very intense light with very easy manipulation, it is interest- ing to reproduce the principal elements in order to facilitate their comparison with other lights. Following are the results obtained by Heim* in the laboratory of the Polytechnic School at Hanover, from a careful study of the principal lights. By means of these results, it is easy to deduce the net cost of the carcel-hour obtained by means of one or another of the lamps enumerated : for this it is sufficient to know the price per gram of the combustible employed. * Lum. til, Vol. XXVI. p. 219. 254 PHOTOMETRY. PETROLEUM LAMPS. Consun iption of Diameter Luminous Petrc louin. Designation. of Burner, mm. with the Horizontal. in German Candles. In Grams per Hour. In Grams per Hour per Candle. Ordinary Argand burner, with round wick . . . Central disc, round burner, 25 45 16.1 12.3 19.2 54.2 53.6 63.4 3.37 4.36 5.30 small size 30 Central disc, round burner, 45 11.1 67.3 61.1 229.0 5.51 3.40 large size 62 45 33.9 228.0 6.72 Kosmos burner .... 30 45 22.9 17.8 84.9 85.5 3.70 4.80 MAGNESIUM LAMPS.* Number of Magnesium Ribbons. Luminous Intensity in German Candles. Luminous Intensity per Eibbon. Without Eeflector. Consumption of Magnesium per Hour per Eibbon in Grams. Quantity of Magnesium per Hour per 100 Candles in Grams. Without Eeflector. With Eeflector. 1 150 3200 150 16.7 11.14 2 237 5880 118.7 16.7 14.10 4 450 8000 112.5 16.7 14.80 6 700 11300 117 16.7 14.15 8 950 17000 119 16.7 14.03 * These magnesium lamps burn magnesium ribbons 2.5 mm. wide by 0.13 mm. thick. The variations of luminous intensity are quite large. The reflec- tor of these lamps increases considerably the luminous intensity in the desired direction. ELECTRIC LIGHTS. GAS-BURNERS. 255 Designation. Inclination with the Horizontal in Degrees. Luminous Intensity in German Candles. Consumption. Of Gas per Hour in Cu- bic Meters. Of Gas per Hour per Candle in Liters. Butterfly ii Argand b t< Auer inc Siemens! it u u u Wenham K n K (t u burner 45 45 45 45 30 45 45 90 25 45 65 90 16.9 17.2 21.9 19.4 14.4 10.5 65.3 46.9 222 162 132 28.4 44.5 45.8 99 152 170 200 202 0.251 0.256 0.239 0.241 0.095 0.104 0.460 0.456 1.621 1.614 1.604 0.249 0.257 0.256 0.686 0.686 0.677 0.685 0.671 14.8 14.9 10.9 12.4 9.60 9.88 7.05 9.75 7.30 9.96 12.2 8.77 5.77 5.58 6.92 4.51 3.98 3.42 3.33 u urner andescence burner . . . u u ntensive regenerative burner it u u 11 U It it 11 U i< u u burner tt (i n l( u (( 155. The measurements of Bailie and Fery * are also very inter- esting. These physicists determined the price per unit of the light furnished by ordinary lighting apparatus ; they adopted the carcel- hour as the unit. The following results were obtained from direct measurements of luminous intensity and consumption of combustible or of energy. The net price is relatively of interest to consult, but it should be calculated anew according to the present conditions, for it was determined by means of the prices quoted at Paris for the combustibles employed. Questions of efficiency are very complex ; it is necessary to state precisely whether the net cost of the carcel-hour applies to the inten- sity measured in a single direction or whether it applies to the mean spherical intensity. For incandescent and arc lamps, and for " but- terfly" gas-burners as well as for flat-wick lamps, the differences are apt to be quite large. * L'filectricien, 1889. 256 PHOTOMETEY. Designation of Source of Light. Inten- sity in Carcels. Rate. Price of the Carcel-Hour at Retail. Observations. Candles. Grams per hour. Centimes. 1. Paraffine candle . . 0.14 8 18.5 Yellowish flame. 2. Perforated candle . . 0.14 10 17.1 3. Star candle .... 0.14 9 12.0 4. Ordinary full candle . 0.15 9 12.0 Oil. 6. Moderator lamp . . 1.04 36 5.6 Double current of air ; rape-seed oil purified 6. Ordinary moderator and filtered. lamp 1.06 42 6.5 Rape-seed oil purified 7. Ordinary moderator and filtered. lamp 0.94 46 6.8 Ordinary oil. 8. Carcel standard lamp . 1.00 42 9.6 Petroleum. 9. Flat wick lamp . . . 0.81 20 2.2 13 mm. wick. 10. " " "... 2.13 62 2.6 50 " " 11. Lamp with two flat \vicks 2.07 63 2.7 25 " " 12. American lamp with- out chimney . . . 1.82 52 2.5 13. Round burner lamp . 1.06 28 2.4 Diam. of the burner 23 mm., ordinary burner, constricted chimney. 14 u u n 1.49 51 3.0 Diam. of burner 25 mm. mushroom burner. 15. " " " . 0.94 30 2.9 Diam. of burner 19 mm. calotte burner, chim- Gas. 16. Ordinary butterfly bur- Liters per hour. ney with knee. ner 0.64 132 6.1 t 17. Bengel burner . . . 1.10 134 3.6 Height of flame 6.5 mm. 18. Zircon gauze burner . 1.39 62 1.3 Much green radiation. 19. Magnesia gauze burner 1.61 191 3.5 " blue 20. Albo-carbon burner . 3.35 135 Incandescent Lamps. "Watts. 21. Edison lamp .... 0.65 29.44 6.8 Below normal rate. 22. Gerard " . . . . 0.72 36.74 7.5 ELECTRIC LIGHTS. 257 Brightness of Radiants. 156. We have not yet dealt with the brightness of radiants. According to definition the brightness or the intrinsic intensity of a light whose luminous intensity is uniform is equal to the quotient of the total quantity of light emitted, divided by the surface of the illuminating part of the source ; we then have Brightness has the same dimensions as intensity of illumination. Two lamps of the same luminous intensity, an incandescent lamp and a carcel lamp for instance, are far from having the same bright- ness. The quantity of light which the first gives is emitted by the small surface S' of the filament, while that from the second is emit- ted by the much larger surface S" of the flame of the carcel lamp ^ we have then To determine the brightness of a source requires the simultane- ous measurement of the quantity of light emitted and the area of the illuminating surface. In his investigations on the lighting of light- houses, Allard was the first to study this element. He determined the brightness of the oil lamps of from one to six wicks employed in the lighthouse service, and obtained the following values expressed in carcels per square centimeter of flame : Number of wicks .... 1 2 3 4 5 6 Brightness ...... 0.197 0.288 0.360 0.415 0.460 0.493 These results allowed Allard to determine the brightness of the sun in the following manner. The intensity of an arc lamp being 200 carcels, he considered this radiant as having the surface of a sphere 1 cm. in diam- eter. The apparent surface of this sphere being 0.7854 sq. cm. (the area of a disc of the same radius), it followed that the brightness of the lamp per square centimeter was 255 carcels, that is, 500 times as great as that of the flame of the six wick lamps. Now Bouguer found that the sun at noon on a clear day was 11,664 times as intense as a candle at a distance of 16 French inches, 258 PHOTOMETRY. [nearly 17 English inches] ; this result corresponds to a luminous intensity 62,280 times as great as that of a candle at a distance of 1 m. Wollaston having found the value 59,850, Allard assumed the mean value 8200 carcels at a distance of 1 m. as producing an illumination equal to that of the sun ; in this number account is taken of atmospheric absorption. Let us consider, at a distance of 1 m., a sphere subtending a visual angle of 32', equal to that of the sun ; the apparent surface of this sphere is 0.6085 sq. cm., and, in order that it may be as brilliant as that of the sun, it should have a brightness of 12,050 carcels per square centimeter. The brightness of the sun is then 47 times as great as that of the voltaic arc and 25,000 times as great as that of the six-wick oil lamp. The following results were obtained by Voit at the time of the photometric measurements of the Munich Exposition : Brightness (in candles per square centimeter). Giroud candle-burner (bee-bougie) 0.06 Argand burner 0.30 Small intensive regenerative Siemens burner .... 0.38 Large " ' " " . . . . 0.60 Incandescent lamps 40.00 Arc-lamps 484.00 The number relative to the arc-lamp does not agree with that of Allard ; the lamp investigated by the latter was without doubt one of greater intensity whose carbons were carried thus to a much higher temperature. We conclude this brief study of the brightness of radiants with the following considerations, which are of real interest not only in the study of radiants, but also in that of lighting in general. Unit of Brightness. 157. There is a fundamental difference between the platinum photometric standard and the candle ; the first gives the luminous intensity represented by the quantity of light which is emitted through an opening 1 cm. square in the diaphragm above the platinum bath, and at the same time the unit of brightness repre- sented by melting platinum. The candle gives only the unit of intensity, and the unit of brightness which should be deduced is in general totally different from the real brightness of the flame. Thus, the surface of a principal section of the Hefner lamp is ELECTRIC LIGHTS. 259 about 2.27 sq. cm. The mean brightness of the flame is then as large as that which it represents ; to form an idea of this 2.27 unit of brightness, the flame should be represented as keeping the same luminous intensity, but reduced to a section - as large. 2.27 We pass, by all degrees of the scale, from the brightness of a surface illuminated at the extreme limit of visibility up to that of the solar disc; these two illuminations are in the ratio of 1 to 1(K Between the two all possible degrees of illumination are found. But their mensuration is still in its infancy; photographs are not yet able to express numerically the brightness of objects which they photograph. They show simply the length of exposure. To express in figures all possible illuminations, either very large or very small numbers are required, according to the unit adopted. If, for instance, we take as the unit of brightness the total intensity of the Hefner lamp, the brightness of melting platinum would be expressed by the number 20, that of the solar disc by 160,000, that of the flame of a candle by 0.4, of the sky by from 0.1 to 1, that of white paper, on which it is possible to read the print, by 0.0006, and that of a white surface at the limit of visibility by a still smaller fraction. The following values were obtained by L. Weber, for various types of brightness, determined for red rays (A = 0.6306 /x) and for green rays (A. = 0.5415 /A) : A. = 0.5415 M I. Brightness of the absolute plati- num standard II. Brightness of the Hefner flame concentrated into a surface of 1 sq. cm III. Brightness of an absolutely white plain surface illumi- nated normally by the plati- num standard at a distance of 1m IV. Brightness of a white plain surface illuminated normally by the Hefner standard at a distance of 1 in. . . . 0.0635 0.0000318 0.00000202 0.049 0.0000318 0.00000516 260 PHOTOMETRY. The following table gives the brightness of a certain number of well-defined objects ; this brightness is represented in terms of the units I. and IV. The first of each bracketed pair of numbers applies to red rays, the second to green. I. IV. 1. Solar disc, outside the atmosphere . . | 2. Sky, near the solar disc -\ 8417 4092 1 5394000000 2025000000 640900 3. Flat carburetted burner, seen at the side | 4. Horizontal white card, at bright noon- f day v. 1 0.509 0.615 0.295 138 494800 326200 304500 189100 68310 5. White card, illuminated normally by f the sun 60 high t 0.144 0.069 92410 34200 6. White cloud, illuminated by the sun . { 7. Flat carburetted gas-burner, seen edge- f wise I- 0.089 0.021 0.073 0.088 57040 10390 4679J 4368) 0.044 28150 9. Bright sky, the sun at azimuths of 60 f and 90 1 0.057 0.05 0.008 28150 33000 3800 10. Horizontal white card, on a dark win- f ter day * 0.0030 0.0010 1945 508 11. Black velvet, on a bright summer day, f same as No. 4 I 12. White card, on which one may read f without difficulty X 0.00059 0.00028 0.000020 0.000015 378 137 10 10 The Mechanical Equivalent of Light. 158. The vibratory motion of the ether produced by a radiant, which is felt on the retina as a luminous sensation, requires for its support an expenditure of energy which it is easy to calculate. The radiant plays the part of a simple transformer of energy. In lights supported by combustion, for instance, the energy is taken from the combustible, resin, oil, or gas ; in electric lamps, it is furnished by the current. Now every transformation is accompanied by losses ; the radiant cannot fail to obey this general law, the losses being proportionately greater as the mode of transformation employed is more imperfect. Every source of light has, then, a determinate ELECTRIC LIGHTS. 261 mechanical efficiency which indicates what fraction of the total energy expended and transformed into a vibratory movement of the ether is capable of producing a luminous impression. This mechanical efficiency is easy to calculate. Following are the details of the calculation for a petroleum lamp and a gas-burner. According to the measurements of Heim, at Hanover, an ordi- nary petroleum lamp, with a round burner 25 mm. in diameter hav- ing an intensity of 16 candles, consumes 3.37 grams of oil per hour per candle. Assuming that the heat of combustion of petroleum is 11,000 calories per kilogram, the lamp consumes then the equiva- lent of 37 calories per hour per candle. Now a calorie corresponds to 41,700 megergs. The energy consumed in the lamp is then 37 x 41,700 = 1,542,900 megergs, which corresponds to a power of = 428.6 megergs per second, or 42.86 watts. Such is the mechanical equivalent of the luminous intensity equal to one candle power, obtained by means of an ordi- nary petroleum lamp. The efficiency increases, i.e. the equivalent energy diminishes, if improved burners of great intensity are used. To calculate the mechanical equivalent of gas-light, we use as a basis also the results obtained by Heim, who found that an Argand burner of 22 candle power consumes 11 liters of gas per hour per candle. The heat of combustion of gas is about 5400 calories per cubic meter. The expenditure of gas corresponds, then, to 59.4 calories per hour per candle, or to 2,476,980 megergs per hour, pro- duced by a power of 68.8 watts. The mechanical equivalent of a gas flame is then 68.8 watts per candle ; it is correspondingly less for intensive burners. The mechanical equivalent of an incandescent lamp is, on the average, 3.5 watts per candle. The mechanical equivalent of the arc-lamp is still lower ; it amounts to about 0.8 watts per candle. The gre^at difference between the efficiency of the two lights just mentioned and that of the incandescent lamp is due to the enormous losses undergone in combustion. The emission of light in these lamps is due to the incandescence of carbon; in the first two the luminous particles are particles of carbon not yet burned, whose incandescence is maintained by the combustion of the gas. There is a loss because of more or less incomplete combustion, and espe- cially because of the convection of heat due to the surrounding air. 262 PHOTOMETRY. In the incandescent lamp the filament is maintained incandescent by the electric current, and, as it is in a vacuum, the loss by convection is null, and the only loss is that due to radiation. The following table contains the values of the mechanical equiv- alent of the candle power obtained by means of the commonest lights ; these values are not absolute, because the consumption in a lamp diminishes considerably when its luminous intensity increases. Candle 86.0 watts per candle. Oil lamp 57.0 " " Petroleum lamp 42.8 " Butterfly gas-burner 93.2 " " " Argand " " 68.8 " " Siemens intensive burner, 230 candle power 45.6 " " ** Incandescent lamp, 16 candle power ... 3.5 " " " Arc-lamp 0.8 "" " Optical Efficiency of Sources of Light. 159. The production of light by a given source is obtained by means of the expenditure of a quantity of energy W which is employed to produce the vibratory movement of the ether. The quantity of energy W radiated by a source of light is composed of two parts ; the one W\ represents the energy of the luminous radia- tions, the other W 2 that of the obscure radiations. Among these three quantities there exists the relation, TF== Fi + TF 2 . rxr The ratio - of the energy of the luminous radiations to that of the totality of the radiations is called the optical efficiency of the source. The efficiency is zero when the temperature of the source is below 400 C., since W l is then equal to 0. It increases rapidly with the temperature. We may employ two methods in measuring this efficiency. The former consists in passing the rays, emitted by the source investigated, successively through a layer of bisulphide of carbon which freely allows all radiations to pass, and through an equal layer of an alum solution, which allows only luminous rays to pass. In these two cases the intensity of the radiations is measured by a thermo-electric pile. The second method is more complicated, but is susceptible of much greater exactness ; it can only be employed for incandescent lamps. The lamp is placed in a calorimeter with thin blackened ELECTRIC LIGHTS. 263 copper sides, filled with water. The whole of the energy radiated by the lamp in the form of heat is absorbed by the water and the metallic sides of the calorimeter. It is sufficient then to measure the elevation of the temperature of the water in the calorimeter in order to deduce the total heat emitted during a unit of time. The calorimeter is then replaced by a similar one of thin glass ; in this case the obscure rays alone are absorbed by the water and by the glass of the calorimeter, while the luminous radiations undergo only a negligible absorption. The elevation of the temperature of the calorimeter is due then solely to the action of the obscure rays. By this method exactness within 0.3 per cent is easily attained. These two methods have been employed by many physicists to determine the optical efficiency of common lights. Tyndall was the first to make researches of this nature. Kecently new measurements have been made by Bl.ittner* of Zurich (1885) and Merritt and Marks t in the United States (1890). The measurements of Blattiier and Merritt concerning the effi- ciency of incandescent lamps have a real interest. The incandescent lamp is in fact the only one whose temperature may be varied at will, since it is sufficient for this purpose to increase the intensity of the current which heats the carbon. We may then vary at will the nature of the light emitted and investigate the light furnished by incandescence passing successively from a dull red color to bril- liant white. All these experimental results confirm the conclusion furnished by the preceding theoretical deductions, viz. that the luminous efficiency should increase with the temperature. This conclusion has received still another confirmation by the measurements of Nakano and Marks upon the luminous efficiency of the voltaic arc. These electricians proved that, for an arc working with a definite difference of potential and intensity of current, the luminous efficiency varies with the inclination of the rays. This fact is very easily explained by the very nature of the voltaic arc. In this lamp the greatest part of the light emitted is due to the upper (positive) carbon, whose temperature is much higher than that of the lower (negative) carbon. The light emitted is due prin- cipally to the positive or to the negative carbon, according to the direction of the ray; that is, it is due to incandescent bodies whose temperature is different. The quality of the light is then different *Lum. til., Vol. XXIII. p. 519. t Lum. l. t Vol. XXXIII. p. 255. 264 PHOTOMETRY. according to the inclination of the luminous rays, and consequently the optical efficiency should also be different. In the following table we have collected the most interesting results of the measurements of efficiency which have been made on light sources ; among the numerous values relating to arc-lamps, we have chosen the highest values obtained with carbons 6 mm. in diameter ; the values really obtained in practice are appreciably less. Designation of Light Source. Per Cent Optical Efficiency. Authority. Hydrogen flame Oil lamp Ordinary gas-burner Swan lamp, 16 candle power, run at 2.6 c.p. tt it, a tt tt tt it 92 t* tt tt tt II .. .. .. I ;J 2 " " " " " " 20.6 " Edison " " " " " " 4.0 " tt (i it tt tt it tt 83 tt u tt tt tt u it tt 1? o tt tt tt it u tt it it 28.6 " Bernstein 32 " " " " 15 " tt tt tt it , . . , Q A 1 1 tt tt t< tt tt u 5Q tt II tt tt tt tttt 1 1 1 1 . . Arc-lamp, inclination t tt tt 10 20 t 30 1 1 < t tt 40 " t tt 5QO tt tt n go " " spherical efficiency Magnesium lamp Geissler tube . 0.0 3.0 4.0 2.3 2.8 3.6 5.2 3.6 4.5 6.2 8.5 42 6.5 7.3 9.9 8.4 12.4 17.4 18.0 18.2 19.8 5.5 16.6 15.0 32.7 Tyndall. Blattner. Nakano. Nichols. Staub. These results show that the optical efficiency of the usual sources of light does not exceed 10 per cent, and that it is generally about 5 or 6 per cent. In other words, in our ordinary sources of light 95 per cent of the energy spent is devoted to producing radiations of the ether which do not affect our eye, that is, radiations whose wave-length is greater than 0.810 /A. From the point of view of the production of light this energy is lost. ELECTRIC LIGHTS. 265 To produce vibrations of the ether whose wave-length is comprised between 0.810 /x and 0.360 /x, we are forced to produce the totality of the vibrations whose wave-length is greater than 0.810 /x. We find ourselves then, according to the happy comparison of Lodge, in the position of an organist who in order to sound certain high notes of his instrument would be obliged to sound all those of the key-board. The low value of the optical efficiency of common radiants is explained by the fact that they are based on the incandescence of carbon and that the temperature of the latter is about the same in all. From the point of view of a physicist we have made no progress in this domain since the beginning of civilization, and the resin torch, of which the savage made use, is, with respect to luminous efficiency, about as perfect as the arc-lamp which spreads the light with profusion in large cities. At most we have succeeded in obtain- ing a mean efficiency of about 6 per cent instead of 3 or 4 per cent. There is still some room then for future progress. Up to the present no attention has been paid to this special point in artificial illumination. All research has aimed at producing electricity as economically as possible ; none has tended to diminish the expenditure of energy in the lamp by a process allowing the pro- duction of obscure rays to be done away with, or at least diminished, without injuring that of the luminous rays. A simple numerical example shows how extravagant are our present methods of illumination. Let us assume that the power necessary for the production of the electric current is furnished by a steam engine whose efficiency does not exceed 10 per cent, under the best conditions. The efficiency of the dynamo-electric machine being 90 per cent, we see that 9 per cent only of the energy accumulated in the coal is transformed into electric energy. If we assume a loss of 10 per cent in the conduc- tors, etc., there remains to be expended in the lamp energy equal to 0.081 of the original energy. But of this energy expended in the lamp 90 per cent is expended in the production of heat ; the remain- ing 10 per cent alone serves for the production of light. The final efficiency is then 0.0081, or 1 per cent only. It is this result which is characterized as brilliant and marvellous. This showing is made by the process of electric lighting. But we easily console ourselves by reflecting that the result is still less satisfactory if we consider other sources of light. 266 PHOTOMETRY. The Artificial Light of the Future. 160. To improve the optical efficiency of light sources, there should only be produced such vibrations of the ether as are susceptible of affecting the retina; that is, vibrations whose wave- lengths are included between 0.810 /x and 0.360 p. Nature has solved this problem in the most perfect manner in the luminous organ of glow-worms and of other luminous insects. This light of peculiar nature has been specially studied by E. Dubois * and by Langley f ; their researches bore on the light emitted by pyrophori, coleopterous insects of the tropics whose photogenic function is well developed. The nature of this photogenic function is still little known; Dubois thinks that it corresponds to a simple physico-chemical phe- nonemon whose activity the insect supports, and which might, for instance, offer some analogy to that which transforms glycogen into sugar in the liver. The light emitted by pyrophori is very remarkable ; it is com- posed almost solely of green and yellow radiations, and its spectrum is continuous, without showing bands or lines. The radiations emitted have a wave-length included between 0.450 /A and 0.650ft, the maximum being at 0.550 ft. We know that the eye is much more sensitive to green and yellow radiations than to the rest of the spectrum. The insect emits, then, precisely the luminous radiations which correspond to this maximum sensibility, which is still another advantageous property of this light from a photometric point of view. Langley determined for four different lights the distribution in the various parts of their spectra of a quantity of energy equal to unity. The following results were reached: In gas-light and that of the voltaic arc, the maximum energy is found at wave-lengths of 1.6 /x. and 1.16/x; i.e. at wave-lengths which affect the retina no longer. We see that almost the whole energy of the spectrum of each of these lights is expended in the infra-red. In solar light and that of the pyrophorus, the maximum energy is in the visible part of the spectrum, at 0.62ft for the former and at 0.57 ft for the latter. This coincidence shows that these two lights of such different * Seances de la Societe de Physique, 1886, p. 138. t Amer. Journal of Science, Vol. XL., 1890, p. 97. ELECTRIC LIGHTS. 267 nature are the best qualified for illuminating. But the second is still better than the first, as the energy expanded outside of lumi- nous radiations is absolutely null, while in sunlight the energy of the infra-red spectrum is not at all negligible in comparison with that of the visible spectrum. If the perfect light par excellence, sunlight, is composed of vibra- tions which are outside of the limits perceptible to the eye, it is because lighting us is not its only object. The energy which the sun sends us by means of the vibratory movement of the ether has also for its object the maintenance of the temperature of the earth between determined limits. In sunlight all the vibrations are use- ful, while in artificial light it is desired to produce only vibrations which affect the retina, and not calorific vibrations; cold light should then be produced. In conclusion we give a brief resume of the researches which have been made with a view to the direct production of this light of the future. All our sources of light, resin torches, candles, gas-burners, arc- lamps, etc., are identical, as we have already remarked. The bright- ness of all these lights is produced by the incandescence of carbon ; they only differ in the temperature to which these particles of car- bon are raised. We must, then, find a substance other than carbon, emitting at the same temperature a much 'greater quantity of light ; i.e. such that the vibrations of its molecules supported by the high temperature to which it is raised would be able to impress on the surrounding ether a much more rapid vibratory movement. This substance once found, the question would have taken a great step forward. It seems that this is not impossible. Nichols has found, for instance, that incandescent magnesium emits light under conditions different from those of carbon. First, this light is much more like that of the sun than that of other sources. With equal luminous intensi- ties the magnesium flame is nearly ten times as brilliant in the violet as the gas flame, and one-half less in the red ; it surpasses that of the arc-lamp also up to the yellow. Some approximate measurements permit the conclusion that the magnesium flame has an efficiency of about 15 per cent, or three times .as much as that of the incandescent lamp at its normal rate. If the luminous substance were carbon, the brightness of the magnesium light would correspond to a temperature much above that of the voltaic arc, while it appears from direct measurement 268 PHO TOMETR Y. that its temperature scarcely exceeds 1400 C.; that is, the tempera- ture of burning gas. Nichols assumes that the law of radiation of magnesium differs essentially from that which governs ordinary cases of incandescence. The luminous vibrations from magnesium oxide are out of pro- portion to the temperature of incandescence, the radiations of short wave-lengfch being very strongly represented. Perhaps there should be considered in the luminous emission of magnesium the phenom- ena that E. Wiedemann designates by the general name of lumines- cence. This word is applicable to all the phenomena known as phosphorescence, fluorescence, etc. It is assumed that luminescence is due to a particular class of molecular vibrations distinct from those which cause ordinary incan- descence ; this mode of vibration has a particular tendency to pro- duce a selection of wave-lengths, one of them always having a ten- dency to predominate. The energy expended in luminescent bodies has then for effect the supporting of molecular vibrations of definite period, these vibra- tions producing in the surrounding ether a vibratory movement of the same period. The whole thing is to find bodies such that molec- ular energy is easily supported in them and which produce waves which correspond exactly to the vibrations of the ether of short wave-length. It seems to us that there is room for research in this direction, the phenomena of luminescence being necessarily at the base of the light-producing power of glow-worms and other luminous insects. In the enumeration of sources of light whose thorough investi- gation might lead to important new results, no mention has been made of the luminous phenomena produced directly by electric discharges. Among these luminous phenomena we should place in the first rank those which are produced in Geissler's induction tubes. The optical efficiency of this source of light has been recently measured by Staub* at Zurich, by means of Bunsen's ice calorimeter. The Geissler tube carefully blackened with lampblack was placed in the ice calorimeter; the quantity of ice melted during a deter- mined time measured the total quantity of heat produced in the tube by electric discharges ; a second measurement made with the tube unblackened. thus allowing luminous rays to pass, permitted the measurement of the quantity of energy corresponding to the obscure radiations. Proceeding in this way, Staub obtained 32.7 * Beiblatter, Weid. Ann., Vol. XIV. (1890), p. 538. ELECTRIC LIGHTS. 269 per cent as the optical efficiency of the Geissler tube. This efficiency is the highest obtained up to the present with artificial sources of light. Unfortunately, the quantity of light thus produced is too small to be used in lighting. The recent work of Tesla gives an exceptional importance to this mode of light production. It seems that this engineer succeeded in making lamps based on the principal of Geissler tubes practical. The electric discharges were obtained by means of high tension alternate currents of very great frequency (20,000 alternations per second). In this way a quite great luminous intensity was obtained. The precise details of this new apparatus and its efficiency are still wanting. Finally, a few words remain to be said concerning a theoretical process of light-production, although this process cannot lead to practical results. The theoretical works of Maxwell have shown that electric phenomena are transmitted by undulations in the sur- rounding ether, and that these undulations coincide with luminous vibrations when their wave-length is sufficiently short. According to this theory light would only be a particular case of electric undulations. The recent experiments of Hertz have con- firmed experimentally this view and have given methods for the pro- duction of electric vibrations of a determined wave-length. These vibrations are produced by the discharge of a condenser in a circuit characterized by its capacity C and its self-induction L. The wave- length of the electric vibrations is then expressed by the equation \ = 2 TT V^C, L being expressed in electro-magnetic units, and C in electrostatic units. This equation allows us to calculate the dimensions of the cir- cuit which would give undulations with wave-lengths A. = 0.6 /x. We find, thus, that the circuit should be of such dimensions that the geometrical mean of its capacity and its self-induction is less than 0.1 p.. This amounts to saying that the dimensions of the circuit should be of the order of molecular dimensions. The electro- magnetic theory of light leads then to a result identical with the preceding. To obtain cold artificial light there must be impressed on the molecules vibrations whose period is equal to that of the luminous undulations, without passing through intermediate vibra- tions of longer period. But the maintenance of the molecular vibra- tions could perhaps be obtained by means of electric undulations produced directly. CHAPTER VI. THE DISTRIBUTION AND MEASUREMENT OP ILLUMINATION. 161. To determine the value of a system of lighting, men have been content for a long time to multiply the number of lamps by the luminous intensity of each, then to divide the total number of light units by the area of the surface lighted. It is needless to say that this method of procedure can only give very imperfect results, for the variations of luminous intensity with the direction of the rays are quite different, according to the light employed ; it is, for instance, inadmissible to compare, in this manner, illumination by gas with that by arc or incandescent lamps. The variations of luminous intensity with the direction of the rays which are not comparable for two gas-burners of different systems, are still less so for a gas- light and an arc-light. This procadure would be about correct if the luminous sources employed emitted the same quantity of light in all directions, or at least if the law of variation of luminous intensity with the inclination of the rays were the same in both. From a practical point of view, what a system of illumination requires, is that the surface to be illuminated should receive throughout its whole extent a minimum quantity of light per unit of surface ; i.e. that its illumination should not fall below the given limit. To compare, for instance, the value of two systems of illu- mination, we must comp ire the illuminations produced by each of them and examine their variations ; the system for which the mean illumination will be the highest, while having the least variations, should be considered the best. The photometric elements of a light being known, we may theoret- ically determine the value of illumination at each point of a given surface, provided the position and height of each light is given ; we may also determine by this calculation what distribution of these lights gives the most favorable illumination. However, this problem is not as simple as it appears ; for account must be taken, in practice, not only of the variations more or less regular in the luminous inten- 270 DISTRIB UTION AND MEASUREMENT OF ILL UMINATION. 271 sity with the direction of the rays, but also of the phenomena of absorption and reflection of light. The influence of reflection is almost insensible in the illumination of a large plane surface, while it plays an important part in the illumination of enclosed places. The absorption of light by the surrounding medium plays no part except in public lighting. We may, moreover, neglect it, for this absorption only takes place, in an appreciable manner, in the case of a fog. Now this case should be considered as an excepticn whose exigencies systems of lighting cannot satisfy. Calculations of the distribution of illumination on a surface are relatively simple when we consider only one luminous source of uniform intensity, i.e. one having the same illuminating power in all directions. But if we consider the general case of many lights hav- ing different illuminating powers according to the direction of the ray, the study of the distribution of illumination is very complicated. Before entering upon calculations of illumination, we should define the unit employed. Intensity of Illumination. 162. The quantity of light dq received by an element of surface dS, whose normal makes an angle i with the direction of the ray, is proportional to the cosine of the angle i (law of obliquity) and inversely proportional to the square of the distance d from the source. We have then the relation (3) We mean by intensity of illumination at a given point of a sur- face the quotient of the quantity of light dq received by the element dS of this surface divided by the area of this element dS. We have, then, = dS d 2 We may thus consider intensity of illumination as the quantity of light received per unit of surface (dS = 1). The distinction between intensity of illumination and illumina- tion, introduced by Wybauw is very useful, for it allows us to speak of the intensity of illumination at a given point, while we may only speak of the illumination of a surface. Intensity of illumination is 272 PHOTOMETRY. a quantity mathematically denned, e = ^, while illumination is a physical or even a physiological notion. It is well to define the unit adopted for intensity of illumina- tion. We must take as the unit of intensity of illumination (e = 1) the intensity of illumination produced with a normal incidence (i = 0) by the unit of luminous intensity (/= 1) placed at a unit dis- tance (d = 1). The unit of intensity of illumination is then connected with the unit of luminous intensity. If the carcel lamp is adopted as the photometric standard, the unit of intensity of illumination will be the carcel-meter ; i.e. the intensity of illumination produced by the carcel lamp at a point situated at a distance of a meter in a horizon- tal plane passing through the middle of the flame. If, on the con- trary, we choose the candle as the standard, the unit of intensity of illumination will be the candle-meter, etc. Hospitalier has proposed to express the intensity of illumination in candles per square meter and not in candles-meter, because the intensity of illumination is inversely proportional to the square of the distance, which the expression candle-meter does not indicate. This criticism does not seem to us well founded ; for the intensity of illumination at a point is independent of the surface considered, since this intensity is the limit of the quotient of the quantity of light received by the element of surface normal to the luminous ray passing through this point, divided by the area of the element as the latter approaches zero. We shall adopt, then, the terms carcel-meter, candle-meter, etc. Let us recall, however, that it has been proposed to give the name of lux to the unit of intensity of illumination, but this name has not yet been sanctioned by usage, and, in particular, it was not adopted by the International Congress of Electricians in 1889. We may, however, employ it, but by applying it to the decimal candle equal to one-twentieth of the absolute platinum standard, which was adopted as the practical unit of intensity by the Congress of 1889. Instead of saying a decimal-candle-meter, we would, then, simply say a lux. Calculation of the Illumination of a Horizontal Plane. 163. Let / be the luminous intensity of a radiant placed at a distance h above the horizontal plane to be lighted. The intensity. of the illumination at any point P (Fig. 84), situated at a distance x DIS TRIE UTION AND ME A S UREMENT OF ILL UM1NA TION. 273 from the foot of the vertical line passing through the source, is given by the formula, e =^ - w 9 being the angle formed with the horizontal by the line joining the source and the point P. L M x FIG. 84. Some very simple transformations allow us to give this formula any of the three following forms : /cos 2 0sin0 /ox ~~ (3) (4) A simple inspection of these formulae allows some very interest- ing conclusions to be drawn. Formula (3), among other things, shows that the variations of illumination in the horizontal plane is proportional to sin 3 0, the light being uniform and at a constant height. This illumination is then a maximum at the foot of the perpendicular, i.e. when = 90. 164. By means of formula (2) we easily determine the height at which the radiant (supposed uniform) should be placed to obtain the maximum intensity of illumination at a distance x\ it is sufficient for this to equate to zero the derivative of the second member of this equation ; we thus obtain the equation, (cos 2 - 2 sin 2 0) = 0, which gives Tang0 = V|. 274 PHOTOMETET. The angle corresponds, then, to 35 16'; the corresponding height h is given by the formula, h = x tan = 0.707 x. (5) To obtain the maximum intensity of illumination at a given point situated at a distance x from the foot of the perpendicular, the light should be placed at a height equal to 0.707 x. Formula (4) allows the solution of an analogous problem : to calculate the radius x of the circumference which receives a deter- minate intensity of illumination e, the height of the light being given. We obtain (6) We may also suppose h variable, and determine the greatest value of the radius x corresponding to a given intensity of illumination e. It is sufficient for this to equate to the derivative of the value of x 2 obtained by means of equation (3). We thus obtain for the condition, = 3 ; = 3 ; = V1' This angle is the same as in the first problem ; it is then equal to 35 16', and corresponds to h = -^ The distance x then becomes, replacing sin0 and cos0 by their values, or>=_?--. -=0.385--; 3V3 * e therefore x = 0.62 \fl. (7) Mean Illumination. 165. Let us consider a part S of the horizontal plane and lay off as an ordinate vertically at each point of the plane the value of the intensity of illumination at that point. The locus of the extremities of the ordinates is a surface which represents exactly the variations of illumination on the surface S. The volume comprised between the latter and the surface, the locus of the extremities of the ordinates, represents the total quantity of illumination of S', this DISTRIBUTION AND MEASUREMENT OF ILLUMINATION. 275 characteristic volume is called the volume of illumination of the sur- face S (Wybauw). The formula which gives this volume of illumination F is simply = CedS, e representing the intensity of illumination of the element dS of the surface S, the integration being extended over the whole surface. Taking account of the dimensions of e and dS, we see that the volume of illumination is a quantity of light ; it is then a new expression to designate a thing already defined. From this point of view we may protest against the introduction of this new term ; but, taking account of the considerations which have led to the expression " volume of illumination," we cannot but approve of this term, which in many cases advantageously replaces the expression " quantity of light." A surface S being given as well as its volume of illumination, we may calculate what the intensity of illumination, supposed uni- form, should be in order that the volume of illumination (limited then by two parallel planes) may be equal to the original volume of illumination. This uniform intensity of illumination is called the mean intensity of illumination or mean illumination) e m ; we have, then, The mean illumination of a given surface S is then the quotient of the volume of illumination F of this surface divided by its area JS, or the quotient of the total quantity of light which falls on this surface divided by its area S. The calculation of mean illumination has many interesting features. 166. We may, for instance, calculate in the following manner the mean illumination of the circular space of radius x having its center at the foot of the perpendicular passing through the light. Let us first consider a circular ring comprised between circles of radii X T and o? 2 , corresponding to rays of light making with the ground the angles 6 l and 2 (Fig. 85). The quantity of light received by this circular ring is the same as that which is received by the zone of the sphere of unit radius limited by the cones of which the circles of the ring are the bases. 276 PHOTOMETRY. For an elementary ring corresponding to an angle dO, this quan- tity of light is represented by the luminous intensity of the source multiplied by the surface of the zone of width dO ; it is then equal L M #1 FIG. 85. to I2ircosOdO. The total quantity of light received by the ring OiOz, or its volume of illumination, is thus = f ''2 ,r/cos 0dA Jo l The mean illumination of the ring is equal to V divided by its surface ; now this surface is equal to J^!_ _^-l. tan 2 2 J The mean illumination is then (8) Making B 2 = 90, we obtain the mean illumination of the circle of radius a;,, having its center at the foot of the perpendicular pass- ing through the source ; we have, thus, JcosftW (9) This formula is general. If we suppose that the intensity of the luminous source is the same in all directions, i.e. if / is con- stant, the formula becomes e = 2 7(1 -sing,) (10) DIS TRIE UTION AND ME A S UEEMEN T OF ILL UM1NA TION. 277 Useful Effect of Illumination. 167. Should we, when we calculate the illumination produced by a source of light, measure this illumination on the horizontal plane or on a plane normal to the rays ? The question is very much debated. In the calculations which precede we have considered the illu- mination on the horizontal plane ; that is, we have multiplied by the sine of the inclination of the rays the illumination produced on a plane normal to those rays. The presence of this factor sin 6 in the formulae constitutes the whole difference between these two methods. Certain very competent specialists in matters of illumination, among others Weissenbruch *, estimate that it is the illumination of the horizontal plane alone which is the element to be considered ; others, on the contrary, among them Wybauw $, are of the opinion that the illuminations of the plane normal to the rays should play the principal part in the distribution of illumination. " It is not, in general, the horizontal geometrical plane, properly so called, which is to be lighted, but the objects on this plane. On public streets it is the passers-by, carriages, the ups and downs of the pavement; and it may be said in general that the bodies which are to be illumi- nated present faces and forms most frequently not in the horizon- tal plane. . . . Although we find ourselves on a material hori- zontal plane, we have no motive for considering a horizontal element rather than any other, and what interests us most, and with most reason, is the maximum illumination which a light can give, at the point where we are, on a surface normal to the direction of the rays." It may be objected to Wybauw's views of the subject that the horizontal earth has a preponderating influence because all objects to be illuminated are found there either stationary or moving about on its surface ; it determines the distance of these various objects from the source of light as well as the inclination of the ray with reference to any surface which might move from one point to another of the ground. * Comparaison de plusieures projets d'6clairage d'un espace dScouvert par grands et par petits foyers, Bull, de la Soc. beige des electr., 1889. J Measure et repartition de Pe'clairment, Bull, de la Soc. beige des electr., 1885. 278 PHOTOMETRY. Suppose, for instance, the ground to be in the form of concentric rings perpendicular to the luminous rays, each receiving a maximum of illumination (0=90); it is evident that the connecting sur- faces are then in the shade, and the horizontal ground shows a cer- tain number of luminous rings becoming narrower and narrower, separated by dark rings becoming wider and wider (Fig. 86). Assuming that the illumina- tion should be measured on the plane normal to the luminous rays, we assume implicitly that a ray oblique to the horizontal plane is as valuable as regards useful effect as a vertical ray, provided that this obliquity does FIG. 86. not exceed a certain practical limit. This limit is confounded, moreover, with the limit of the distances beyond which no account is taken of the illumination, which has become too feeble. Illumination on the Horizontal Plane and on the Normal Plane. 168. We may then define the useful effect of illumination c pro- duced by the light of intensity /, placed at the height h above and at the horizontal distance x from the element dS of the horizontal plane, by the formula 1 dS, (11) = to which we may also give one of the following forms : 7cos 2 , e e = dS, (12) (13) The useful effect of illumination, introduced by Wybauw, being thus simply defined, we may study the importance of this concept from a practical point of view. DIS Tit IB UTION AND ME A 8 UREMENT OF ILL UM1NA TION. 27 9 The preceding formulae show that the useful effect at a given point of the horizontal plane is to the intensity of illumination at this point as 1 to sin#; i.e 1 e consequently the useful effect is always greater than the intensity of illumination. If, then, we calculate the illumination produced by a given source, basing it on the useful effect, we obtain too favorable a result. TLe following considerations, based on precise experiment, show that the results furnished by calculations based on the intensity of illumina- tion are somewhat too small. In fact, the calculations relative to intensity of illumination are based on the law of the cosine, which is not exact, giving only a poor approximation in the majority of cases. We should remember, further, that the horizontal plane appears proportionately more illuminated as its reflecting power is greater; a black board appears less illuminated than a white one, and objects are distinguished less clearly from the former than from. the latter. The illumination obtained on a given surface will be proportionately more advantageous as the quantity of light emitted by the surface after reflection is greater. It has been generally sup- posed that the law of photometric emission was strictly exact, or, at least, as exact as possible. But recent investigations by Seeliger, at Munich, have proved that the majority of the substances employed in buildings do not follow, even remotely, this theoretical law. There are often found errors of 20 per cent, with inclinations of from 20 to 25. It follows from this that calculations of illumina- tion, based on the law of the cosine, cannot give results strictly exact ; we are forced to be content with results which are more or less approximate. It seems to us useful, then, to take account practically of the two methods, that of illumination properly so called, and that of useful effect. We shall consider the intensity of illumination deduced from the fundamental photometric laws as the lower limit of illumination, and the intensity of useful effect defined by Wybauw as the upper limit of this same quantity. This point of view is purely empirical, but it seems sufficiently justifiable since it allows account to be taken of the arguments which militate in favor of one system or the other. 280 PHOTOMETRY. 169. We may calculate the total quantity of useful effect received by a circle of radius x } whose center is directly below the light, in the same way that the total quantity of illumination is calculated. The quantity of useful effect received by a circular ring of radius x and of width dx is equal to 2-n-Ixdx Consequently, the total quantity of useful effect received by the circle of radius x, corresponding to the obliquity O l} is Ixdx or sin0 Integrating, we obtain immediately, supposing /constant, or, in common logarithms, 2 Xi = 7.2347 log In the same way, S fc = 7.234 1 log [1 + cot 2 0J. These values of 2 become infinitely large for a^ = oo, or for O l =Q. This result was easy to foresee, for it is supposed that the intensity of useful effect diminishes proportionately to x 2 , while the surface illuminated increases proportionately to -n-x 2 . Because of this result the introduction of the notion of useful effect of a light source has been criticised ; these criticisms are not well founded, for Wybauw made the express reservation that the intensity for useful effect may only be substituted for intensity of illumination up to a certain limiting incidence ; it is then this value of the limiting incidence, corresponding to the radius x 0) which should be taken as one limit of the integration when it is desired to calculate the total useful effect of a light. Following are some particular values deduced from the formulae : 2 = 7, whn x = 0.6124ft ; i.e. when = 58 31'. In the same way 2 = TT /, when x = 1.3115 h ; i.e. when = 52 40'. D1S TRIE UTION AND ME A S UREMEN T OF ILL UMINA TION. 281 When x = h, we have 2'= 2.1777, and when x li V3 = 1.73 h, we have double the preceding value ; i.e. 2 = 4.354. The expression 2 or 2 X represents a volume of useful effect assuming for this volume the definition corresponding to that of volume of illumination ; the limit- ing surface of this volume may also be called the surface of useful effect. We may also define the mean useful effect e TO , in the same way as the mean intensity of illumination, as the quotient of the volume of useful effect divided by the surface illuminated ; consequently, the mean useful effect of a circle of radius x whose center is directly below the light is _ 7.234 /log (l + cot 2 0) ~~ Introduction of the Real Luminous Intensity into the Calculation. 170. It was supposed in the preceding calculations that the lu- minous intensity of the source considered was uniform. Now this hypothesis is not realized by any luminous source, as has been seen in the preceding chapter ; we may, however, assume that it is true for some of the usual lights, for alternate-current arc-lamps, and even for continuous-current arc-lamps with opalescent globes. However, with bare continuous-current arc-lamps, it is impossible to assume uniformity of luminous intensity. Calculations made on this hypothesis would lead to completely erroneous results. If it is desired to calculate the intensity of illumination or the useful effect at a point, we must take the value of the luminous intensity corresponding to the inclination at which the rays of light striking the point considered are emitted. Thus, for a point at a distance from the foot of the perpendicular equal to the height, the maximum intensity (0 = 45) should be taken. For a point at a distance 2 h, the luminous intensity corresponding to 28 should be taken, etc. 171. Knowing the meridianal curve of the photometric surface of the radiant, we may determine by graphical methods the intensity of illumination at any given point of the horizontal plane. The fol- lowing method is given by Loppe* (Fig. 87). If the luminous intensity in the direction LA is equal to K ' LA, and if the height h is proportional to LM, i.e. if h equals K 1 LM, * tflectricien, 1890, p. 936 282 PHOTOMETRY. FIG. 8T. the intensity of illumination at the point B of the horizontal plane passing through M will be K-LA (K'.LB)' cos HBL. Lay off LB' LB, join A and B', and through M draw a paral- lel to AB''j we obtain a point C on LA ; join C and B', and through Jlf draw a parallel to 05' ; we obtain a point Z), and we have LB) If through D we draw a horizontal until it meets at E the vertical through B, we shall have = 2^1 Y cos / HE = LD cos HBL From the preceding relations it follows that e = J^-HE = * (K'-LM) 2 k Proceeding in the same way for directions L (1), L (2), etc., we TT obtain a curve 1' 2' E 3', etc., whose ordinates, multiplied by , DISTRIBUTION AND MEASUREMENT OF ILLUMINATION. 283 give the quantity of light received by the horizontal plane, and whose abscissae, multiplied by K'f = --\ give the horizontal projection of the distance from the point considered to the light. The construc- tion then allows us to find, by a simple reading of the scale, the illu- mination at a point of the horizontal plane situated at any distance below the light. By means of this curve shown at 1" 2" E" 3", etc., we may easily find the radii of the circles on whose circumferences are the points of the plane whose intensity of illumination is equal to a given quantity e. To do this we lay off from M l on MJ5 1 a length M^I so as to have Through / we draw a parallel to the axis of x ; this cuts the curve at L and K. The points of the plane situated at distances K 1 IK and K' IL from the foot of the perpendicular passing through the light will receive from the latter a quantity of light equal to e^ We may then draw on tracing paper circles corresponding to illuminations 1, 2, 3, etc., and find the illumination produced by any number of lights. In case of a light of uniform intensity, to each value of the inten- sity of illumination on the horizontal plane there corresponds only a single circle, while in the case of a bare continuous-current arc- lamp, two circles correspond to each intensity. This graphical method offers, further, the following great advan- tage. It has been seen in the preceding chapter that the photo- metric surface of continuous-current arc-lamps is of nearly the same shape whatever be the intensity of the light. The preceding figure may then serve in all cases if the coefficients /fand K' are changed every time, so that the maximum luminous intensity may be repre- sented by the expression K-LA and the height of the light by K' LM. It is sufficient then to determine each time the particular values of the coefficients ./if and K'. We cannot insist too strongly on the necessity of employing, in calculations of illumination by continuous-current arc-lamps, the real luminous intensity and not the mean spherical or the maximum intensity. The mean spherical intensity gives too small values for the illumination, while the maximum intensity gives too great values. 284 PHOTOMETRY. 172. The curves in Fig. 88 represent these different cases. There were taken as abscissae horizontal distances and as ordinates intensities of illumination expressed in luxes (decimal-candles meter), the light being assumed at a height of 1 m., and supposing 1. The luminous intensity uniform and equal to the maximum intensity 1000 decimal candles (curve J.); 2. The real luminous intensity as given by Fig. 82 (curve B), 3. The luminous intensity uniform and equal to the mean spher- ical intensity 352 decimal candles (curve (7). These curves permit an important conclusion to be drawn. Below a certain value of the intensity of illumination correspond- ing, for instance, to a distance equal to five times the height of the lamp, the diminution of the intensity of illumination is very small for a considerable increase in the distance. But these illuminations 100 FIG. 88. are too small to take account of. In all calculations of illumination, then, we should not exceed a certain limit, and especially is it neces- sary, as Wybauw says, "to avoid long and minute calculations which the result does not warrant." Using as the basis the normal diagram of the luminous intensity of the continuous-current arc-lamp, Wybauw made a diagram (Fig. 89) which allows the easy calculation of the quantity of light received (volume of illumination) or of the useful effect of illumi- nation, corresponding to a circle of radius x whose center is directly below the light. In this case direct formulae become very compli- cated and graphical methods alone allow the practical solution of the problem. The two upper curves A and A' represent the cal- culations of useful effect, while the lower curves B and B' refer to intensity of illumination. The curves A and B are those of a uni- form light of 1000 candles ; the curves A' and B' those of an arc- lamp whose maximum intensity is 1000 candles. DISTRIBUTION A.ND MEASUREMENT OF 1LLUMINA TION. 285 A mere inspection of the drawing is enough to show its use. Let us suppose, for instance, that there is required the volume of illumination furnished on the ground, in a circle of 30 in. radius, by a light placed at a height of 10 in. whose maximum intensity is 2000 candles. The distance being equal to 3, we have for the abscissa x = 3 ; the corresponding ordinate y is 5.877. Then the volume sought is 5.877 x 2000 = 11,754. If in place of an electric lamp, one had a light of uniform inten- sity of the same power, the diagram would give 13,232. This number is not exactly that which would be obtained by applying the formulae. The reason of this is that the diagram was drawn by Wybauw, who considered as uniform the illumination in 3.5 4- Axis of X the circle of radius h about the foot of the perpendicular passing through the light, the intensity of this uniform illumination being equal to the intensity at the foot of the oblique line of 45 inclina- tion. In fact, in practice, the illumination on the base of the 45 cone is always more than sufficient. If we have to do with lights of uniform intensity, the superabundance of illumination in the cir- cle is of no use and need not be taken into account ; it is an inevita- ble and forced excess. With electric lights, the nearness, the effect of the reflector and of diffused light, render this illumination more than satisfactory. This way of calculating is unfavorable for lights of uniform intensity. Moreover, it is not allowed by all specialists, and the elimination of the superabundant illumination in the calcu- lation of the mean intensity is not to be recommended, as we shall see later. 286 PHOTOMETRY. It is well understood that these data have to do only with bare lights. Account should be taken of the loss occasioned by electric light globes. It may be assumed as 30 per cent, so that a 200 carcel light with a globe becomes in calculations a 140 carcel light with a bare flame. It is to be remarked, further, that the distribution of light about a lamp with a globe is not entirely similar to that of a bare lamp. The ellipse of the diagram becomes less elongated ; the difference may even be quite considerable, as has been seen in the preceding chapter (148). To calculate the volume of illumination furnished by a light on a ground of irregular limits, we shall proceed by calculating first the volume for the greatest circle of radius r described about the foot of the perpendicular passing through the light wholly within the poly- agonal ground ; then the volume for the fraction of the ring rr', 360 x being the angle at the center subtended by the part of this ring included in the ground ; then for the second ring r'r", etc. The value for each whole ring is given immediately by the diagram. Each of them has, in fact, for a volume of illumination the difference between the two extreme ordinates corresponding to the abscissae -, , etc., h h multiplied by 7, the maximum intensity of the light expressed in candles. We may evidently, by suitably spacing the circles, obtain such degree of exactness as is desired. These calculations are very simple, and their exactness is sufficient for all practical purposes. 173. We could not better conclude this study of the distribution of illumination than by giving a resum of the solution which Loppe has given of certain particular problems in which he supposes it to be true that the luminous intensity is uniform. The formulae which he arrived at, notwithstanding this restriction, are interesting enough to find place here. Illumination of a Surface, the Lights being placed at the Angles of Equal Squares. 174. Suppose four lights of the same uniform intensity, placed at equal heights above a horizontal plane, at the angles of a square ; we are to find the point of the plane within the square where the intensity of illumination is minimum. If ABCD are the projections of these lights (Fig. 90) placed at DIS TRIE UTION AND MEA8UREMEN T OF ILL UMINA TION. 287 a distance 2 a from one another, choosing the axes of co-ordinates as indicated in the figure, the total intensity of illumination e at a point is given by the expression in which Solving for maxima and minima of this expression, we find that the point of intersection of the diagonals of the square receives the minimum quantity of light when h < aV3. This point, on the con- trary, has a maximum illumination when 7i>aV3. The first case, 7i2a. 288 PHOTOMETRY. Illumination of a Given Surface corresponding to a Minimum of Expenditure. 175. The solution of the following problem leads to some inter- esting conclusions which we will enumerate. The problem may be stated as follows : To illuminate a horizontal plane by means of lights of uniform intensity, in such a manner that the intensity of illumination at any point may be at least equal to a given quantity e , employing for this the least energy possible. There are two cases to consider. 1. A surface is to be illuminated. In this case, the lights will be placed at the corners of squares. 2. A street is to be illuminated. In this case, most usually the lights are placed alternately, on one side and the other of the street. 176. To illuminate a surface. The majority of the light which falls at a point within one of the squares comes evidently from the four lights which are in projection in its corners. If 2 a is the side of one of the squares, we have seen that when the condition 7i<1.732a is realized (which occurs ordinarily in practice), the point of minimum illumination is at the point of inter- section of the diagonals. The spacing of the lights is to be calculated so that at this point the intensity of illumination produced by the four lights shall equal e ; then if the influence of the other lights is not negligible, they may be placed a little farther apart. In the latter case, the following conclusions are none the less valid, for the greatest part of the light is due to the lights placed at the four corners. If h is the common height of the lights above the plane, 2 a the distance between the lights, or the side of the square, and I their uniform luminous intensity, we have for the intensity of illumination at the intersection of the diagonals the formula sip.^ (15) (h 2 + 2 a 2 ) * This formula affords a solution of the following problem. DISTRIBUTION AND MEASUREMENT OF ILLUMINATION. 289 177. The height h of the lights above the plane being given, to choose a lamp of such luminous intensity 7 that the energy expended may be minimum. The number N of lights necessary to illuminate a surface S being the expenditure in watts is given by the formula 4 a 2 In the case of arc-lamps of medium intensity B may be taken as a constant ; in the case of lamps of great intensity, B is a function of 7. To solve the problem in the case where B is constant, it is suf- ficient to find the minimum of : we thus obtain 4 a 2 (16) We take for / the practical value nearest the value found, and we find 2 a, by equation (15). We shall increase the distance between the lights a little, as needed, if the influence of the other lights is not negligible. If, after having calculated 7 and 2 a, we find that the condition h < 1.732 a is not fulfilled, we must see whether the illumination at the various points reaches a given value e , for in this case we know that the illumination due to the four lights is maximum at the point of intersection of the diagonals. 178. The same formula gives also the solution of the following question. 7 is given, to find such a value for h that the energy expended, that is the number of lights employed, may be a minimum. The number of lights is given by the relation From (15) we obtain, making f Y=.B, \ e o / whence N = 290 PHOTOMETRY. The minimum of N corresponds to the maximum of Bh* - h 2 . Equating the derivative to 0, we have fc = ^W Y= 0.877 JI. \3J \e J \ e<) If, after having calculated a by equation (16), we find h > 1.732 a, we should proceed to the verifications indicated above. 179. To illuminate a street. The lights (Fig. 91) are placed at ABC. The points D and E on the perpendicular passing through the middle of AB receive from A and B the minimum of light, if h<2a. Let AD = a as before, and we write the fundamental condition 2Ih (17) We may then solve the same problem as in the case of illuminat- ing a surface. For instance, h being given, to determine / so that the energy to be expended may be minimum. The number of lights is inversely proportional to a ; the expendi- 7? T T ture in watts will be proportional to or to In the case where a a B is constant, we obtain from (17) the value a = - ft 2 )*, putting = C. DISTEIB UTION A ND ME A S UREMENT OF ILL UMINA TION. 291 We should then obtain the minimum of the expression I which gives j.SfijJ^.awMF. (is) We take for I the practical value which is nearest the calculated value and deduce a from equation (17). In case that the influence of more distant lights is not negligible, a may be slightly increased. 180. To solve the second problem, J is given to find h. It is noticed that the number of lights is inversely proportional to a ; in order to have the minimum of energy expended, a or a 2 must then be made maximum. From (17) we obtain a 2 = D*h* - h 2 , putting D = - e<> Equating to the derivative with respect to h, we obtain Practical Points. 181. The photometric calculations relative to the lighting of uncovered places enable us to solve a considerable number of partic- ular problems. We have studied a number sufficiently large to show the method of procedure in each special case. It remains to compare the results of the preceding formulae with those obtained in practice. The height of the lights is an important element in all systems of lighting. The distance between lights being equal to 2 a, the illumination at a distance a from the light is maximum when the height is given by the formula ^STST* vr-"- ItfflfiBtiTT] 4*rffefi$ 292 PHOTOMETRY. This height is rarely adopted in practice. With lights 100 m. apart, we should have towers 35 m. high. Esthetic considerations relative to the decoration of streets forbid the adoption of such high lights. In certain cities in the United States, where these consider- ations have not as much weight as in Europe, very powerful lights are frequently employed placed on the top of latticed towers 30 to 40 in. high, or even higher. In Europe the height of the lights is generally between 6 and 15 m. We must distinguish, with a view to the disposition of the lights, between the illumination of streets and that of open spaces. Lighting of Streets. 182. The lamps may be placed in two ways : either alternately on the two sides of the street, along the edges of the sidewalk, or in a line with the middle of the driveway. The former arrangement is used in gas lighting ; the latter is that which has been used for the illumination of the great boulevards of Paris. To begin with, we give some data as to the intensity of the mean illumination by gas, in the principal streets of Paris in 1889 : Rue Royale ........... 1.6 lux. Rue de la Paix .......... 1.5 " Place de rOp^ra . . . . ..... 0.7 " Avenue de I'OpSra ........ 0.43 " Rue du Quatre-Septembre ...... 0.43 " All Paris ............ 0.05 " Using arc-lights, illumination along the middle of the street is the most rational. The other system of illumination, along the edge of the sidewalk, is only allowable with lights whose luminous intensity does not exceed 100 candles. The intensity of illumination at a horizontal distance x from the foot of the lamp-post is expressed by the formula Ih The height h being given, as well as the value of the intensity of illumination below which we should not go, it is easy to calculate the distance between the lights. W T e thus obtain the following table, which gives the distances between two lights at heights of 6, 10, and 14 m. and of different uniform intensities corresponding to different minima of intensity of illumination. ' DISTRIBUTION AND MEASUREMENT OF ILLUMINATION. 293 DISTANCE BETWEEN Two LIGHTS IN METERS. 7=500 J=600 7=700 7=800 7=900 7= 1000 Minimum Dec. Dec. Dec. Dec. Dec. Dec Intensity of Candles. Candles. Candles. Candles. x Candles. Candles. Horizontal Illumination h h h h h h 6 10 14 6 KI 14 6 10 14 6 10 14 6 10 14 6 10 14 0.5 44 50 54 47 54 58 50 57 62 52 60 67 54 64 68 56 65 71 1 34 38 39 37 41 43 39 44 46 41 46 49 43 48 52 44 50 54 2 26 28 26 28 30 30 30 33 32 32 35 35 31 36 37 34 38 39 Lighting of Squares and Large Open Places. 183. If, for streets, and particularly for narrow streets, lights of small intensity are preferable to powerful lights, it is quite different for the lighting of public squares and large open spaces. In the first case, the reflection of light on the house fronts increases greatly the illumination in the neighborhood of each light ; the contrast may be so strong that the parts situated midway between appear to be in darkness. In the second case, there can be no question of any action of reflection by vertical walls. Thus it is well to employ intense lights placed at a considerable height. The lights may be arranged quincuncially or at the corners of equal squares, if an illumination as uniform as possible is desired. As to the height of the lamps, following are some figures sanctioned by practice : Height of the Lamp. 10 meters. 15 " Maximum Luminous Intensity. 240 carcels (10 amperes). 328 " (13 " ). 390 490 (15 (18 18 20 The distance between two consecutive lights is determined accord- ing to the minimum admissible for intensity of illumination. From the point of view of the uniformity of illumination of a great surface, it is evidently advantageous to employ a great number of small lights. For it is then easier to satisfy economically the conditions of minimum illumination. But, as Weissenbruch has re- marked, the comparison of two systems of illumination of the same surface is not correct if we observe only the single condition of minimum illumination. Account should also be taken of the mean illumination. 294 PHOTOMETRY. The mean intensity of illumination is always greater with large than with small lamps, for the former give an intense light in the vicinity of their supports. In other words, large lamps always give some superabundant light* in the neighborhood of the lamp. Should account be taken of this superabundant light in the calculation of mean intensity, or should there be assumed, for the intensity of illumination of the circle about the lamp, the value corresponding to the 45 ray ? Some authorities are in favor of the second alternative, among others Wybauw, who made a correction relative to it in the diagrams of Fig. 89. Others, on the contrary, think with reason that so much illumination cannot be neglected. The parts superabundantly lighted are only an advantage, for they form veritable secondary sources of reflected light. However, if two systems of illumination are to be compared, there should be introduced the mean intensity of illumination cal- culated by taking into account the total quantity of light received by the surface, giving it an importance at least as great as that of the minimum illumination. Weissenbruch has demonstrated the necessity of introducing these two elements, mean intensity and minimum intensity of illu- mination, in calculating the lighting of railway stations ; this con- clusion applies equally in all cases when we have to do not only with minimum but with the most intense illumination. It is difficult to give exact values of the minimum intensity of illumination. These values vary too much according to circum- stances. The state railways of Belgium allow, for example, an intensity of illumination of -^ of a carcel meter for the lighting of stations. This number is somewhat too small, particularly as compared with the values of the mean illumination of the principal streets of Paris, lighted by gas. Employment of Reflectors. 184. With arc-lights, the intensity of illumination is very much greater than the minimum required ; it would then be advantageous to diminish the quantity of light received just below the lamp in order to carry it to a greater distance. To do this, reflectors of particular form must be employed, which render the illumination of the horizontal ground sensibly uniform. Among apparatus of *Lum. l., Vol. XL pp. 149, 244. DISTRIBUTION AND MEASUREMENT OF ILLUMINATION. 295 this kind, the dioptric lantern of Trotter * seems to solve the prob- lem in the most perfect manner. Trotter combined his reflectors with a view to solving the prob- lem of the uniform illumination of the ground. This problem may be stated as follows : It is required to illuminate by a single central light a plane circular area, so that if this area be divided into rings of the same surface, each of these rings may receive the same quantity of light. These successive rings have radii which increase proportionally to VI, V2, V3, etc. It is sufficient for this that the rays emanating from the source of light and making equal angles with one another, may be so directed that the tangents of their new inclinations with the vertical may increase as Vl, V2, V3, etc. Trotter obtains this result, at least approximately, by aid of a hexagonal lantern whose faces are formed by ribbed strips of glass ; the form of these ribs is carefully determined by the preceding, and their section may be obtained graphically. The results obtained with this apparatus are very satisfactory. Preece, who has tried it, speaks of it in the highest terms. The intensity of illumination is increased at a certain distance from the lamp, but is diminished in a much greater proportion just below it. Unfortunately the shape of the glass is very complicated, which greatly increases the cost. For this reason its use has not become general. Recourse is, however, often had to reflectors, but without an exact determination of their form. Plain or ribbed ones are chosen, generally of sheet iron enamelled white. But the only object of this apparatus is to throw upon the ground the rays of light directed upward which otherwise would be of no practical use. Like Jasper at the Electrical Exposition of 1881, we may also use quite large white discs, which are placed horizontally above the lamp, and which play the double part of reflectors and secondary sources of light by means of diffusion. It is in this category that Elster'sf new reflectors should be placed. The following table gives the means of passing rapidly from illumination by lamps of given intensity / to other systems in which there are employed lamps whose intensity is double, triple, etc., that of the former. It is applicable to the lighting of a hori- * Lum. EL, Vol. XIV. p. 98. t Elektr. Zeitschr., 1891, 438. 296 PHOTOMETRY. zontal surface by a single lamp, by a series of lamps in a straight line, by lamps arranged at the corners of squares, and quincuncially. The unit of length is the radius of the circumference of the given minimum illumination. One Light. Lights in a Straight Line. Lights Quincuncially. Luminous Intensity. Height. Radius of the Circumference of Minimum Illumination. Height. Distance between the Lights. Distance between the Lights. I h r h 2a= 2r I 0.70 1.0 1.65 3.0 4.2 2 0.98 1.4 2.31 4.2 5.9 3 1.19 1.7 2.86 5.2 7.3 4 1.40 2.0 3.30 6.0 8.4 5 1.54 2.2 3.63 6.6 9.2 6 1.68 2.4 4.07 7.4 10.4 7 1.82 2.6 4.40 8.0 11.2 8 1.96 2.8 4.62 8.4 11.8 9 2.10 3.0 . 4.95 9.0 12.6 10 2.24 3.2 5.17 9.4 13.2 Lighting of Enclosed Places. 185. If the problems of lighting a horizontal plane by many lamps is difficult, that of lighting enclosed places is particularly complicated. The lighting of a room depends, in fact, on many factors, among which the luminous intensity of the lamps employed does not play so preponderating a part as would at first be supposed. Outside the effect of lighting, there is another element to be con- sidered, which Wybauw calls the effect of illumination ; this is indeed a consequence of lighting properly so called, but is not related to it in any definite proportion, and it often becomes a factor of consider- able importance in modifying one's judgments of the lighting of rooms. The numerous flames of a chandelier give the impression of an intensity of light much greater than that of a single flame which might have the same power. Two gas flames or two electric lamps may have very different intensities ; and yet when they are not absolutely side by side, they will produce the same effect upon our eyes. The light of a simple candle is seen at night at a considerable distance, at even 500 m., while its effect as a source of light is not appreciable on objects placed at this distance. It is the same with DISTRIBUTION AND MEASUREMENT OF ILLUMINATION. 297 a white wall, lighted at night. A row of lanterns close together, on the front of a house during a f&te produces at a certain distance absolutely the same effect of illumination as a row of gas-lights whose jets are, however, much brighter. These effects of illumination have no common measure with the intensity of lighting, and yet they contribute in an important degree to the final effect obtained, and account should certainly be taken of them. Diffused light is also an important element in the lighting of enclosed places. As a means of illumination it is given an impor- tance which it does not have when measured in comparison with simple direct light. In a room lighted by gas-burners with opal globes, the eyes deceived by the appearance labor under the impression of an illu- mination much greater than the real ; it is necessary to take up a newspaper or book to appreciate the insufficiency of the light which these globes give. A diffusing surface when lighted throughout its extent becomes a source of light ; it gives out light at all points and in all direc- tions, in contrast to a simple reflecting surface, such as a mirror. If a mirror is placed behind a light, the room will appear to be lighted by two lights ; if the mirror is replaced by a white wall at a suitable distance from the light, the effect will be much more satisfactory, although in reality the light reflected by the dull surface may be much inferior as to its intensity to that reflected by the mirror. All bodies reflect light, but with an exceedingly variable inten- sity, according to their distance from the source, their color, and finally the degree of roughness or polish of their surfaces. This diffused light is a power auxiliary to the effect of lighting produced by the direct light. It is diffusion which makes daylight so much superior to all artificial light. The latter illuminates objects in a single direction only, leaving lateral or opposite faces in a strong shadow which the light, reflected by surrounding objects, can only slightly diminish. It is quite difficult to take account of the increase in illumination produced by light diffused by the ceiling and walls of a room. We may, however, obtain an approximate idea, as Mascart has shown, in the following manner. Diffusion is nothing but ordinary reflection on a surface whose irregularities are of the same order as, or are greater than, the wave-length. We should then assume that the total fraction of light diffused is analogous to the fraction of light whioh would be regularly 298 PHOTOMETRY. reflected by a polished surface, and which may, under certain circum- stances, reach 90 per cent. Without giving a numerical value to the coefficient / of diffusion, let us suppose that a system of lights placed in a closed room emits a total quantity of light Q. A definite portion of this light is absorbed by the walls, another portion fQ, being diffused, is distrib- uted anew in the room; the second diffusion gives likewise a quantity of light f 2 Q, etc., so that the total light used is )= Q :y The mean brightness of a sheet of paper placed in all possible positions will be, if the walls are black, proportional only to the quantity Q of light emitted by the sources, and with walls of reflect- ing power /, proportional to the quantity Q The increase of illumination is then represented by the ratio : For instance, if /= 0.95, the room would appear twenty times as bright as with black walls. We do not arrive at this extreme value with certainty, but the advantage of having white walls must not be very far short of it. [See Appendix H.] 186. When we have to do with installing the lighting of a large hall, architectural and other necessities determine the height and location of the chandeliers and lights ; their number is also fre- quently the result of the same necessities. We may determine the intensity of these lights or the number of them on each chandelier so as to obtain a minimum intensity of illumination, n luxes for instance, in the horizontal plane 1 m. above the floor. It is this plane which is usually chosen in such cases, in preference to the plane of the floor itself. The minimum intensity of illumination evidently does not apply to the corners of the room ; it is clearly not intended, in fixing this limit, to consider individual points of the space to be lighted. The line of minimum illumination will be a curve inscribed in the poly- gon formed by the sides of the room and lying without the circles of greatest possible radius inscribed in the polygon having the lights for centers. If the location of the lights is obligatory, it frequently happens that the distribution of light leaves much to be desired with respect to uniformity. In a room whose ceiling is divided into three parts DISTRIB UTION AND ME A S UEENEN T OF ILL UMINA TION. 299 by two beams, the location of the lights is obligatory ; the necessi- ties of decoration and lighting frequently produce similar constraints. From a practical point of view, the reflecting action of a ceiling may be replaced by that of an imaginary light directly above the real light and whose intensity is equal to a certain fraction k of that of the latter. Wybauw made some experiments to determine k in a medium-sized room. He found that he might assume, without great error, k = 0.5. The introduction of the imaginary light into the calculations allows the problem to be treated mathematically and certain conclu- sions to be drawn. But the want of exactness of the coefficient k does not allow much value to be given to conclusions from calcula- tions of this kind. We are obliged to keep to empirical indications and data furnished by practice. Dimensions of the Eoom in Meters. Number of Lights. Height of the Lights above the Floor in Meters. Number of Square Meters per Light. Length. Width. Height. 4.6 4.7 3.8 2- 3 2.0-2.2 8.4 5.6 5.6 4.4 5- 6 2.0-2.4 5.7 7.5 7.5 5.3 9- 12 2.5-2.8 5.3 10.0 10.0 6.9 16- 20 2.8-3.1 5.5 12.5 12.5 9.4 25- 30 3.5-3.8 5.6 5.7 15.7 12.5 40- 45 4.0-4.4 5.8 12.8 18.8 14.0 60- 70 4.7-5.3 5.4 22.0 20.0 15.7 100-120 5.6-6.3 4.0 TJppenborn* has given as a resume of his experiments, and from direct measurements, the preceding table which shows the number and height of the lights (IGc.p.) to be employed to illuminate places of different dimensions. By examining this table, we see that the distribution of illumina- tion corresponds on the average to one light for each 5.5 sq. in., for rooms of very different heights. We should conclude from this that these places may be sufficiently lighted, but not equally lighted, especially as the illumination due to light diffused by the ceiling varies with the height of the place. The rate of one light to 5.5 sq. m. is high enough so that differences of illumination might have passed unnoticed because of the very abundance of light. * Centralblatt fur Elektrotechnik, Vol. III. p. 244. 300 PH TOMETR Y. 187. It is interesting to discuss how the quantity of light should vary with the geometrical dimensions of a room in order that the illumination may not change. We shall consider only the cases of closed rooms with ceilings of moderate height. At first sight it seems as if, in order to give an equal illumina- tion to two rooms geometrically similar, their quantities of light should be in the ratio of their surfaces or of the squares of homolo- gous dimensions. If we imagine a single source at the center of a sphere, the quantity of light received per unit of surface is inversely propor- tional to the square of the radius ; the illumination will then remain the same if the intensity of the source is proportional to the square of the radius. It is quite otherwise in practice. Fontaine determined that, in the majority of cases, the quantity of light should be proportional to the volume of the room, and not merely to its surface. For a drawing-room, for instance, whose walls are of medium tint, it has been observed that a quantity of light of 0.5 candle per cubic meter gives a satisfactory illumination, using suitably distributed lamps of from 10 to 16 candle power. It should be remarked that a room is never entirely empty. It contains furniture and objects of some kind or other which are so many obstacles to the propagation of light; the supports of the lamps, chandeliers, candelabra, etc., intercept also a considerable part of the light ; finally, the air itself has not the perfect trans- parency which the law of inverse squares of the distances assumes. We may sum up all these causes of loss of light by assuming that the efficacious illumination due to a light ceases at a determi- nate distance, within which it would have spent its full effect. This limiting distance varies much with the conditions of prac- tice, the number of obstacles, and the clearness of the air. It is not the same for a theatre, whose central part is entirely empty, as for a drawing-room full of furniture, or a factory crowded with machinery, etc., and it is very much less at the time of a fog. The following table, prepared by Mascart*, gives some data as to the way in which public halls were illuminated at different epochs, and shows that illumination has pursued a very rapid progressive course, especially in recent years. * Bull, de la Soc. int. des tflectr. Vol. V. p. 103. DISTRIB UTION AND ME A S UREMENT OF ILL UMINA TION. 301 Dimensions. Total Number of Candles. Number of Candles. Floor Area. Square Meters. Volume. Cubic Meters. 5 er Horizon- tal Square Meter. Per Cubic Meter. Salle des Glaces of the Palace of Versailles. In 1745 . . 720 720 720 440 672 400 530 1295 300 165 496 257 195 350 250 240 90 200 96 9360 9360 9360 3520 7392 9200 8000 24000 2460 1350 4067 3600 1350 5600 4800 3500 1000 3250 1400 1800 4000 8000 1000 6000 11140 4720 18720 4320 720 7560 3600 720 2470 2360 2340 1900 3200 1970 2.50 5.35 11.10 2.28 8.93 27.85 8.90 14.46 14.40 4.36 15.24 13.98 4.36 7.06 9.44 9.75 21.10 16.00 20.52 0.19 0.43 0.85 0.28 0.81 1.21 0.69 0.78 1.75 0.53 1.86 0.56 0.53 0.44 0.55 0.67 1.90 0.98 1.40 1873 " 1878 .... Salle des Fetes at Com- piegne. In 1888 Opera House (used as ball- room). Foyer Body of the house . . . Sta^e City Hall (Balls of 1888). Fete-Hall Dinin o -Hall Conservatory Grand Salon Side Gallery Keserved Salon .... Theaters (Body of the House). Odeon Gaite . . . . Comedie Frangaise. . . Palais-Royal . Porte-Saint-Martin. . . Renaissance Lighting of Factories. 188. The preceding figures show how vague are the data rela- tive to the lighting of enclosed places. The problem resolves itself into determining in advance the number of candles per square meter of horizontal surface, or per cubic meter of the total volume, and 302 PHOTOMETRY. into distributing the lights of moderate intensity so as to obtain the most uniform distribution of light. If certain engineers, who have had much to do with the instal- lation of electric light in factories are to be believed, calculations based on the fundamental photometric laws alone should not govern the installation. A correspondent of V Electricien gives, for instance, the following data concerning the lighting of thread mills. These establishments require a great deal of light; the rooms are of large dimensions, and contain numerous machines quite uniformly distrib- uted and of the same dimensions. There is scarcely a plant in which less than one 12-ampere lamp is employed for from 180 to 200 sq. m. ; this case supposes a great height of room, and ecru or light- colored thread. The maximum illumination found corresponds to a 10-ampere lamp for 80 or 100 sq. in. Among the looms, the minimum is one 12-ampere lamp for 120 sq. m. For white, for ecru, and for light colors, a very good illu- mination is given with one 10-ampere lamp for 75 or 85 sq. m. For dark materials, it is necessary to reckon on at least one 10-ampere lamp for 50 sq. m. The data which Uppenborn gives on this subject agree practically with the preceding. A rsum6 is given in the following table. Nature of the Space to be Illuminated. Number of Square Meters per 10- Ampere Lamp. 2000 sq. m. Train houses 1400 " " Founderies (general lighting) 500-600 " " " (special lififhtin 01 ) . . 200 250 " " 200 " " 200 " " In a factory, a very simple way of verifying the quality of the lighting consists in asking workmen distributed uniformly in the room whether they see better in one place than in another, when they have been accustomed to the lighting for several months. The quality and quantity of the production of the shop is also an indication of the quality of the light. These indications are hardly scientific; they may have some value, however, but it is necessary to confirm them by direct measurements of the illumination. DISTEIB UTION AND MEASUREMENT OF ILL UMINA T1ON. 303 189. Let us add that the object of artificial lighting is not always to distribute light in a uniform manner in all directions. For manual work or for reading it is often desired to concentrate the light at certain points. In artistic lighting we seek to produce a harmonious blending of lights and shadows which puts into relief figures, ornaments, and decoration, so that we are obliged to sacrifice a part of the general brightness. The concentration of light on particular points gives a certain importance to a very simple and useful apparatus, ths reflector, employed with all the common radiants. Almost all commercial reflectors have a very annoying defect as respects the illumination of a room ; viz. the top of this apparatus is narrowed to such a point that it hinders in great part lighting the ceiling. Now the ceiling is of great utility in the lighting of a room ; the room is better lighted and appears still more so because of its illumination. When fixed lights are employed, reflectors which are sufficiently open above should be used. The form of the reflecting surface is of little importance when it is desired to have the light reflected downward in all directions ; then the conical form, with an angle at the base of from 35 to 45, is perfectly suitable. But the generatrix of the surface of the reflector is not a matter of indifference when the flame is to light the surface of a table principally. In this case it is not well to use those conical reflectors which bring the rays together in too great quantities just below the light, to such an extent as to form at the middle of the table an intensely luminous ring, to the detriment of the lighting of the rest. A reflector should be chosen whose surface forms a zone of an ellipsoid of revolution, its axis being coincident with the axis of the light. We may without inconvenience replace the ellipsoidal zone by a spherical one of like dimensions. Intensity of Illumination required for Reading. 190. The study of the common reflector leads us naturally to give the values of the minimum illumination required for reading. These values are in no respect exact, for they are dependent greatly on the physiological conditions of the eye. The intensity of the illumination should be proportionately greater as it is desired to read more rapidly and with less fatigue. Javal has determined that on a printed page whose intensity of illu- 304 PHOTOMETRY. mination is one candle-meter, with good sight one can read No. 7 characters at a distance of 70 era. from the page, No. 8 characters at 80 cm., and No. 9 characters at 90 cm. Leonard Weber found that the rapidity of reading is in direct ratio to the degree of illu- mination. Thus a person who reads six lines of a book when the intensity of illumination is 2 candles-meter, reads twelve lines of it in the same length of time if the intensity of illumination is doubled. These conclusions are naturally true between certain limits only. Cohn, a well-known German hygienist, estimates at 50 candles- meter the illumination produced by daylight on a well-exposed table ; he further estimates that the minimum hygienically necessary for reading and writing without abnormal fatigue should be 10 candles-meter. Measurement of Illumination. 191. In case of doubt as to the value of a system of lighting, recourse must be had to measurements of the intensity of illumina- tion at different parts of the space lighted. The methods have been studied in Chapter III. ; it is proper, however, to return to them to indicate the modifications which they must undergo so as to be adapted to this particular kind of measurements. It is evident that two illuminations are equivalent when the same object, submitted alternately to one and the other, appears to have the same brightness and produces the same effect on the retina. We know that the eye is to some extent unfitted to give a photo- metric judgment in the general case, but the information which it furnishes acquires more precision when the quantity of light is reduced to the minimum necessary for a determined operation. It is this which happens in the case of reading. For instance, if it is desired to read continuously a text printed in a certain size of type and placed at an invariable distance from the eye, it is necessary that the light diffused by the paper should not fall below a definite minimum for each person's sight. When the illumination falls below this limit, reading is no longer continuous ; one is obliged to read each word separately, and generally seeks to bring his eye nearer the paper, to increase the apparent angle of the characters, always provided that the accommodation of the eye allows them to be seen with clearness. Such are, as we have seen, the elements of photometric methods based 011 visual acuteness. These methods are the simplest, and are sufficiently precise for measurements of illumination. DISTRIBUTION AND MEASUREMENT OF ILLUMINATION. 305 If the experiment is repeated with characters of unequal size, it is readily recognized that, for the same distance of the eye, the illumination should be proportionately more intense for continuous reading as the letters become smaller. A sheet of paper with a series of phrases printed in characters of different types will then furnish a true measure of illumination. It is very easy to construct an apparatus on this principle. Schutte has invented, for the use of photographers, a very ingenious small apparatus which may also be of service in measurements of illumination, and which it is easy to modify advantageously. The apparatus called a lux-meter by Wybauw is much like that of Schutte. This apparatus consists in a disc movable about its center and formed of superposed layers of translucent sheets ; it is next divided into a series of sectors of which the number of layers increases in a progressive manner, which permits more or less absorption of the light which traverses it at this point. Behind this disc is a screen which has on a like circumference a series of characters of unequal sizes. The type of the characters which may be read by transparency with a given fraction of light gives an approximate measure of the illumination. Use of Weber's Photometer. 192. Weber's photometer ( 53) is also made with a view to measurements of illumination, while using as a standard the acetate of amyl lamp. The apparatus is used in the following way for this particular object: At the point and in the direction along which we wish to measure the illumination we place a plate of opal glass or a sheet of white cardboard, whitened with white lead ; the movable tube B of the photometer is then directed at this card. In order that only the light diffused by this cardboard may enter the tube, care must be taken that the angle formed by the generatrix of the cone having its apex at the center of the opalescent disc of the tube B and its base on the cardboard, shall not exceed 60. Further care should be taken that no direct light enters the tube and that the illumina- tion of the cardboard is not modified by the presence of the observer. Suppose, first, that the diffused light and that of the acetate of amyl standard have the same color. Equality of illumination of the two plates may be produced. 306 PHOTOMETRY. Suppose e to be the intensity of illumination of the white card- board ; because of absorption in the cardboard, a quantity y e only will reach the dull disc of the tube B, and this having a coefficient of transparency a, the illumination of the field of the movable tube is equal to arje (a should be made equal to 1, if the tube B is used without the dull disc). Let be the distance, expressed in meters, of the luU dull disc of the fixed tube from the flame of the lamp, and let (3 be the coefficient of transparency of this plate. The illumination of the field of the fixed tube is then, designating by / the candle power of the lamp, . I e= ^rjry =/ uoo; We have, then, for the setting for equality of illumination of the two plates, aye = e', whence we conclude __! 10000 = p,10000 art' d 2 d* If / is expressed in candles, this formula gives the intensity of illumination in terms of the candle-meter. The constant C" is determined by illuminating the cardboard screen by a light of known intensity placed at a determined dis- tance. We then calculate the intensity of illumination e of the cardboard placed normally to the rays of light, and measure the intensity which corresponds to a reading r of the apparatus. We have then ^,10000 = 12 ' whence 0WJEL 10000 The apparatus may also be used without the white screen by replacing the cap of the tube B by a disc of opal glass designated by the letter /x ; we then give to the apparatus and the movable tube such a position that the disc /u, occupies the point, and is normal to the direction with respect to which we wish to measure the illumi- nation. DISTRIB UTION AND MEASUREMENT OF ILL UMINA TWN. 307 We next determine the reading 8 of the apparatus for which the two fields are equally lighted. We have then _n 10000 -- The constant C" is determined in the same way as C 1 by means of a light of known intensity. These two methods cannot be used when the color of the diffused light differs from that of the light of the standard (acetate of amyl lamp). We should then make two settings d r and d g , interposing a red and a green glass in the path of the rays. We then find in the table on page 89 the coefficient k corresponding to [ ] and calcu- late e by means of the formula e , = K7 , 10000 WY or by means of according as we employ an independent screen or a fixed disc with a movable tube. Beside Weber's photometer, we may employ that of Mascart also, of which Pellin has, moreover, constructed a portable form. There are also other forms of portable photometers based on the employment of ordinary Bunsen or Foucault screens. It is very simple to modify this apparatus so as to make it portable without sacrificing too much of its precision. APPENDIX BY THE TEANSLATOES. APPENDIX. A. [See page 39.] It is difficult to see how this statement can be true. If L, M 9 and R coincide, all of the three conditions mentioned above must hold : by 1, the spot must disappear on the left face of the screen ; by 2, the spot must disappear on the right face of the screen ; and by 3 there must be equal contrasts on both sides. If all of these conditions hold for the same position of the screen, it would seem that the condition of equal contrasts must be satisfied by an absence of contrast on both sides ; that is, the spot can be neither bright on a dark background nor dark on a bright background. B. [See pages 50 and 95.] The Lummer-Brodhun photometer may be used to compare the luminous intensities of an arc and an incandescent lamp, but, as the two regions of the luminous field seen in the telescope will appear light blue and light yellow, it is quite difficult to decide exactly when the two regions are equally bright. However, if the mean of several settings is taken, the probable error will not be large. If now the side of the screen toward the arc-light is covered with light yellow paper, and the other side with light blue-green paper of just the right tint, the two regions in the telescope will appear to be of uniform color, when a balance is obtained. The setting will now probably be different from what it was with the white screen. If calculations of the relative intensities of the two light-sources are made from both sets of readings of the photometer, a coefficient of relative absorption may be obtained. This coefficient will remain practically constant on comparing the arc-light at various inclinations with the incandescent lamp. As the color of the light emitted by the arc-lamp varies with the inclination, it is not possible to choose tints of paper that will make 311 312 PHOTOMETRY. the two regions appear of exactly the same color at all inclinations. The variation in color will, however, not be the cause of much error in the observations. This variation in color may be compensated by varying the voltage of the incandescent lamp. If this is done, it is necessary to have previously measured the intensity of the incan- descent lamp at various voltages. If these results are plotted in a curve, the intensity of the incandescent lamp at any point within the limits of calibration may be read off directly. In a particular case, the arc-lamp was suspended as described at the bottom of page 190. The mirror used was found to absorb 17.25 per cent of the light incident on it. The luminous intensities of the arc-lamp measured with the white screen, and with the yellow and blue-green screen were in the ratio of 763 : 1000. To calculate the true value of the intensity of the arc-lamp, the value calculated from the settings of the photometer with the colored s\ fT/*O papers must be multiplied by - ' = 0.92. Covering the sides of the screen with the yellow and the blue- green paper can, of course, give no additional absolute accuracy to the photometric measurements ; it, however, adds greatly to the comparative accuracy of the results, as it makes it possible to meas- ure the relative intensities, under various conditions, with great precision. On reversing the photometer, it is necessary to reverse the screen also, so that the yellow side may still be toward the arc-lamp, other- wise one part of the field will appear a deep yellow and the other a deep blue. C. [See page 143.] The following regulations for testing the Hefner lamp are taken from Schillings Journal f. Gasbeleuchtung u. Wasserversorgung, 1893: " The second (technical) department of the Imperial Physico-Technical Institute undertakes the testing and certification of Hefner lamps according to the following directions consistent with agreements made with the Ger- man Gas and Water Association : 1. " The object of the test is to ascertain whether the candle power of the lamp, after being lighted for at least ten minutes, equals the normal value of one Hefner unit as fixed by the standard of the Institute, the lamp burn- ing pure acetate of amyl, and the flame reaching the mark of the gauge fur- nished with the lamp. APPENDIX. 313 2. " Hefner lamps constructed as described in the appendix, are admitted for examination, provided they have one of the flame-gauges there described and the name of the manufacturer as well as the lamp number stamped on the lamp. "3. " The test consists " 1. In ascertaining the accuracy of the more important dimensions. " 2. In the photometric comparison of the lamp, using its own flame- gauge, with the standard of the Institute. "4. " A certificate will be issued " 1. If the test shows that the thickness of the wick-tube is not more than 0.02 mm. larger or 0.01 mm. smaller than the normal, and that its length does not differ by more than 0.5 mm. and its inner radius by more than 0.1 mm. from the normal, and that, after the gauge has been put on, the distance between the top of the wick and the edge of the gauge does not differ by more than 0.1 mm. from the normal. " 2. If the candle power does not differ from that of the standard by more than 2 per cent. 5. " If a certificate is issued, the current number and the Imperial Eagle will be stamped on the following parts of the lamp : 1, the vessel ; 2, the burner ; 3, the wick-tube ; 4, the flame-gauge ; 5, the control-gauge. "In the certificate will be given the results of the test, showing the deviation of the candle power from the normal within 1 per cent. "6. " The fees charged are : " 1. For testing and certifying a Hefner lamp with a flame-gauge, m. 3.00 " 2. For testing and certifying a Hefner lamp with a sight and an optical flame-gauge 4.50 " 3. For testing and certifying a Hefner lamp with a second wick- tube and a flame-gauge 4.50 " 4. For testing and certifying a Hefner lamp with a second wick- tube and both flame-gauges . . 5.50 Charlottenburg, March 30th, 1893. " Imperial Physico-Technical Institute, " v. HELMHOLTZ." 314 PHO TOMETR Y. Next there follows a description of the lamp substantially as given on p. 135, which we omit. CERTIFICATE FOR HEFNER LAMP No.. "The lamp is marked "It has a v. Hefner-Alteneck vane-sight, a Kriiss optical flame-gauge, a second wick-tube, and a control-gauge. " The dimensions of the wick-tube and the control-gauge differed from the normal within the limits allowed for certification. " The candle power found by photometric measurement was using the vane-sight using the optical gauge For wick-tube a for wick-tube b Hefner units, " As none of the deviations exceeds the limits allowable, the lamp was stamped with the number of the certificate and the Imperial Eagle on all parts mentioned hi the regulations. " A description of the lamp and directions for the use of the lamp, the flame-gauges, and the control-gauge are given with the certificate. " Charlottenburg, ^ 189-. " Physico-Technical Institute, " Department II. "(Signature)." " The back of the certificate contains extracts from the preceding regu- lations as well as other information concerning the granting of the certifi- cate." "DIRECTIONS FOR USE. "The Wick. "The quality of the wick has in general no influence on the candle power. It is only necessary to take care that it fills the wick-tube entirely, but on the other hand, is not pressed too tight. We therefore find it most convenient to use a sufficient number of thick cotton threads laid together. But since such loose threads are easily displaced and form loops inside the reservoir and clog the gearing, wicks woven on the outside are frequently used. There is no objection to their use as long as they fulfil the condition of filling the tube without being too tight. APPENDIX. 315 "THE ACETATE OF AMYL. " Care must be taken in procuring acetate of amyl for the Hefner lamp, the commercial article often containing substances which render it useless for photometric use. The acetate of amyl should, therefore, be obtained from a reliable firm, and it should be stated on buying it, that it is to be used for photometric measurements. " In order to facilitate the purchase of good acetate of amyl, the German Gas and Water Association has undertaken to procure sufficient quantities of suitable acetate of amyl, and after testing it, to sell it at its office (Hofrat Dr. Bunte, Karlsruhe) in sealed bottles containing from 1 liter upward. " If it is not desired to make use of this opportunity of obtaining tested acetate of amyl, it is best to first examine, as to its usefulness, other acetate of amyl. For this, the following tests, in most part due to Dr. Bannow, are the most useful. According to him acetate of amyl may be used for meas- urements of candle power if the following conditions are fulfilled : " 1. The specific gravity must be from 0.872 to 0.876 at 15 C. "2. In distilling the acetate of amyl in a glass retort, at least 0.9 of its quantity should pass over between 137 and 143 C. " 3. The acetate of amyl should not decidedly redden blue litmus paper. " 4. If we add an equal quantity of benzine or carbon disulphide to the acetate of amyl, the substances should mix without becoming milky. " 5. If we shake in a graduate 1 cc. of acetate of amyl with 10 cc. of alcohol 90 per cent (Tralles) and 10 cc. of water, a clear solution should result. "6. A drop of acetate of amyl should evaporate on white filter paper without leaving a greasy spot. " The acetate of amyl should be well corked, and if possible kept in the dark." Then there follow directions for the use of the lamp. D. [See page 188.] This value for the absorption, 1.8 per cent, is altogether too low- to be believed. It is so given, however, in the original paper com- municated to the (London) Electrical Review, of July 13th, 1888. It may be a misprint for 18 per cent. In 120, p. 191, will be found values of the absorption for two mirrors. These values range from 15 to 32 per cent for a single reflection. In Appendix B another mirror is mentioned, for which a value of 17.25 per cent was found. From these values it would appear that 1.8 per cent for a double reflection is undoubtedly in error. 316 PHOTOMETRY. E. [See page 202.] Theory may indicate (a) that the horizontal sections of the pho- tometric surface should be similar curves, or (b) that the variations in the various vertical planes should follow the same law, which is a quite different assumption. In (a) there is only one horizontal section, that is, the section passing through the light-source, which is directly concerned with luminous intensity ; the other horizontal sections include no radii vectores, and it is along these alone that the luminous intensity is laid off. The assumption made in (b) is not supported by the facts. An examination of the figures given in Table III., p. 205, shows that there is no fixed ratio between the variations of the numbers in the two columns for each class of lamps. This may be due to varia- tions in the form of the filament, or to irregularities in the shape of the bulb. But whatever be the reason, it is evident that in practise we may not make this assumption, except as a gross approximation. F. [See page 228.] A very interesting and instructive paper on arc-lamps was read before the Electrical Congress at Chicago in 1893, by Professor W. E. Ayrton, F.R.S., etc. In this paper Professor Ayrton threw considerable light on the subject of 139. This paper will be found in the Proceedings of the Congress, about to be published by the American Institute of Electrical Engineers. It is not at present available. G. [See page 236.] The following extracts from a paper by A. P. Trotter* will be found of interest in considering the form of the polar curve express- ing the connection between inclination and candle power. In Mr. Trotter's paper the angles are measured with respect to the axis of the carbons " It has been assumed by many persons that the hollowing of the crater of the positive carbon tends in some unexplained manner to concentrate and throw the light downward. It is evident that the lower or negative * The Electrical fieview (London), May 6, 1892, p. 583. APPENDIX. 317 carbon intercepts a good deal of the light ; but there speculations appear to have stopped. A little consideration will show that the effect is precisely and identically the same as though the end of the positive carbon was flat. No tilting of an incandescent or other luminous surface can make it brighter ; and, on the other hand, if it is covered with a thin imperfectly transparent layer, as in the case of the atmosphere of the sun, the edge will appear less bright than the middle of the disc. The quantity of light emitted by an incandescent disc in any direction is proportional to the amount of surface visible from that direction. That is to say, candle power varies then as the cosine of the inclination. "Cosines plotted as a polar curve give a circle passing through the pole. . . . The candle power of the crater of an arc-lamp should, then, if plotted as a polar curve, coincide with part of a circle. Any deviation from the circle must have some cause. Two such deviations are observed and their causes are easily recognized. " The full curve in Fig. 92 represents the mean of a large number of observations made [by Wybauw], no less than 26 different arcs having been tested. The cosine of 60 being one- half, the area of the crater seen from this direction is one-half of that of the full circle; the candle power is one- half of that emitted by the crater ; and the length of the radius vector corre- sponding to 60 may be taken as the radius of the circle. "The light due to the negative carbon is clearly shown as an excess above the circular curve; there is in- deed nothing else to which it can be due, except the red-hot walls of the crater [and the arc proper]. " At about 60 the curve of candle power begins to fall off, and this is due to nothing else than the shadow of the lower carbon, which intercepts more and more of the light as we pass to smaller angles, until, if the carbons be of the same diameter, no light is thrown in a vertical direction. " In considering the real meaning of the latter part of the curve, the author drew a number of views of a pair of imaginary carbons, projected at various angles. The elliptical area of the crater in each view was calcu- lated, and he found that these areas, plotted as radii of a polar curve, gave a curve closely resembling the well-known candle-power curve of the arc. It follows that, if this be proved to be true by experiment, the candle power per square millimeter of the crater is constant. 318 PHOTOMETRY. "The author communicated this result to Professor S. P. Thompson, and asked if he would see whether actual experiment would confirm it." Such actual experiments were carried out by Mr. C. F. Higgins. Concerning the relation between the apparent area of the crater and the luminous intensity Mr. Trotter says : " A straight line cutting the axis at 100 candle power seems to fit the results. This may be explained by the light which is emitted by the red- hot and glowing parts of the carbon. These were not included in the measurement of area ; the true crater only was measured." Mr. Trotter found the intrinsic intensity of the crater to be 42600 candles per square inch, or 64 candles per square millimeter. H. [See page 298.] The following values for the reflecting powers of various sur- faces were obtained by Dr. W. E. Sumpner. See Phil. Mag., Feb- ruary, 1893, p. 81. He says concerning them : "In the majority of cases the numbers given are approximate only, as there seemed no object in aiming at great accuracy. The first four surfaces referred to in the table, viz. thick white blotting-paper, white (rough) cartridge-paper, tracing-paper, and tracing-cloth, were, however, carefully tested, and the numbers obtained represent the mean of many observations. "REFLECTING POWERS. Per Cent. White blotting-paper ... 82 White cartridge-paper ... 80 Tracing-cloth 35 Tracing-paper 22 Ordinary foolscap .... 70 Newspapers 50 to 70 Tissue-paper (one thickness), 40 " " (two thicknesses), 55 Yellow wall-paper .... 40 Blue paper 25 Dark brown paper .... 13 Per Cent. . . 4 40 to 50 . . 20 . . 30 22 Deep chocolate paper Plane deal (clean) " " (dirty) . . . Yellow cardboard . . . Parchment (one thickness) " (two thicknesses), 35 Yellow painted wall (clean), 40 " " " (dirty), 20 Black cloth 1.2 Black velvet 0.4 * INDEX. Absolute standard and secondary standards, The, Absorbing media, The employment of, Absorption of mirrors, Acetate of amyl lamp, The, Actions of light, The photometric, Various, Alternate current arc-lamps, Appendix, Arago's photometer, Arc-lamps, Argand lamp, The, Arnoux's photometer, Artificial light of the future, 108 66 191 136 9 7 251 309 69 224 111, 149 50 266 Ayrton and Perry's dispersion pho- tometer, 57, 61 Benzine lamps, 135 Bouguer's photometer, 27 Brightness of radiants, 257 Brightness, The unit of, 258 Bnnsen's photometer, 35 Bunsen screen, The construction of the, 43 Theory of the, 38 Candle, Combustion of the, 119 Candle-burner, The Giroud, 144 Candles, 118 Carbon, Standards based on the em- ployment of, 160 Carbons, The nature and manufac- ture of, 230 Carcel lamp, Dimensions and work- ing conditions of the, 113 Practical value of the, 116 Standard, The, 111 Color of the light, Sensibility of the eye with, 12 PAGE Compensation photometers, 67 Complementary color. Employment of media of, 93 Composition of the light emitted by various sources, 14 Conroy screen, 34 Consumption of candles. Measure- ment of the, 127 Of the principal sources of light, The rate of, 253 Contents, ix Cornu's method, 58 Crova's method, 63, 91 Crova's spectro-photometer, 101 Dessendier's registering photome- ter, 97 Diaphragms, Photometers based on the employment of, 52 Theories and properties of, 52 Dibdiu's radial photometer, 183 Dispersion lenses, Properties of, 54 Distribution and measurement of illumination, 270 Diverging lenses, Photometers based on the employment of, 52 Duboscq's photometer, 69 Efficiency of incandescent lamps, 223 Elster screen, 45 Employment of reflectors, 294 Enclosed places, Lighting of, 296 English candle, The, 122 Equipment of photometric laborato- ries, 181 Factories, Lighting of, 301 Foucault's photometer, 28 Foucault's screen, Construction of, 31 Franklin Institute tests, 204 111) 320 INDEX. Fundamental photometric law, The, 1-5 Fusion point of stearine, The, 129 Gas-burners, 255 German candle (Vereinskerze) , The, 122 Giroud standard, 143 Grosse's mixture photometer, 74 Hefner lamp, 136 Prism, 36 Height of the flame, Measurement of the, 126 Heterochromatic photometry, 77 Holophotometer,Vernon-Harcourt's, 186 Horizontal intensity of incandes- cent lamps, 198 Horizontal plane, The illumination on the, 278 Illumination, The measurement of, 304 Of a given surface correspond- ing to a minimum of expen- diture, 288 Of a surface, the lights being placed at the angles of equal squares, The, 286 Of a horizontal plane, The, 272 On the horizontal plane and on the normal plane, The, 278 The useful effect of, 277 Incandescent lamps, 195 Incandescent lamp, as an absolute standard, The, 160 As a secondary standard, The, 161 The most economical life of, 220 Lamps, Manufacture of, 196 Intensity of illumination, 271 Light, 5 Of lighting required for read- ing, 303 Joly screen, 45 Kriiss's compensation photometer, 72 Krtiss screen, 43 Kriiss prism, 37 Lambert's photometer, 26 Lamp, Argand, 111, 149 Carcel, 111 Hefner, 136 The Giroud standard, 143 Lamp, Vernon-Harcourt pentane standard, 152 Lamp-holders, Incandescent, 192 Lamps, Arc, 224 Benzine, 135 Incandescent, 195 Magnesium, 254 Law, The fundamental photometric, 1-5 Lighting of enclosed places, 296 Factories, 301 Squares and large open places, 293 Streets, 292 Lion's photometric balance, 97 Luminous intensity of incandescent lamps, 198 Standard candles, 130 Variations of, with energy ex- pended, 209 Variations of, with life and rate, 213 Lummer and Brodhun's screen, 47 Mace de Lepinay's method, 82 Magnesium lamps, 254 Mascart's photometer, 64 Masson's photometer, 100 Mean horizontal intensity, 18 Mean illumination, 274 Mean spherical intensity, 18, 20 Of arc-lamps, 239 Of incandescent lamps, 202 Measurement of illumination, 304 Mechanical equivalent of light, 260 The unit of light, 110 Methven standard screen, 149 Millis's arrangement, 189 Minimum of expenditure, Illumina- tion of a given surface corre- sponding to a, 288 Mirrors, the absorption of, 191 The employment of, 190 Munich candle, 122 Napoli's photometer, 60 Normal plane, The illumination on, 278 Opal globes and reflectors, The em- ployment of, 242 Optical efficiency of sources of light, 262 Pentane standard, Vernon-Har- court's, 152 INDEX. 321 PAGE Personal errors, 175 Petroleum lamps, 131, 254 Photometers, 25 Photometer, Arago's, 69 Arnoux's, 50 Ayrton and Perry's, 57, 61 Bouguer's, 27 Bunsen's, 35 Compensation, 67 Cornu's spectre-photometer, 104 Dessendier's registering, 97 Diaphragm, 52 Dibdin's radial, 183 Diverging lens, 52 Duboscq's, 69 Elster's, 45 Foucault's, 28 Grosse's mixture, 74 Holophotometer, Vernon-Har- court's, 186 Joly's, 45 Kriiss's compensation, 72 Lambert's, 26 Lion's photometric balance, 97 Lummer and Brodhun's, 47 Mascart's, 64 Masson's, 100 Napoli's, 60 Polarization, 67 Pupillary, 98 Relief, 33 Rousseau's radial, 185 Rumford's, 26 Selenium, 96 Spectro-photometers, 100 Thompson and Starling's, 34 Vernon-Harcourt's holophotom- eter, 186 Villarceau's relief, 33 Visual acuteness, 77 Weber's, 85, 305 Wheatstone's, 100 Wild ' s pol ari zation , 69 Wybauw's compensation, 72 Photometric action of light, 9 Bench, 178 Elements of luminous sources, 17 Standards, 106 Photometry of arc-lamps, The his- tory of, 232 Heterochromatic, 77 Room, 174 PAGE 160 67 227 291 v 1 Platinum, Standards based on the employment of, Polarization and compensation pho- tometers, Potential difference in the voltaic arc, Practical points, Preface, Principles of photometry, Pupillary photometer, 98 Reading, Intensity of light required for, 303 Real luminous intensity, The intro- duction of, into the calcula- tion, 281 Reflectors, Employment of, 294 Regulators and arc-candles, 231 Relief photometers, 33 Rousseau's radial photometer, 185 Rudorff's mirrors, 36 Rumford's photometer, 26 Schwandler standard, 160 Selenium photometer, 6 Sensibility of the eye, 10 Spectro-photometry, 100 Standard candles, The luminous in- tensity of, 130 Star candle (Bougie de 1'Etoile), 121 Streets, The lighting of, 292 Tint of an incandescent lamp, Cal- culation of the, 221 Toerpler screen, 43 Thompson-Starling screen, 34 Translators' preface, iii Use of Weber's photometer, 305 Useful effect of illumination, 277 Vacuum, Influence of degree of, on luminous intensity, 212 Variations of the luminous inten- sity of arc-lamps, 233, 244 In the luminous intensity of the candle with the height of the flame, and the consump- tion of combustible mate- rial, 123 Various actions of light, Photome- ters based on, Of* 322 INDEX. PAGE Vernon-Harcourt's holophotometer, 186 Pentane standard, 152 Villarceau's relief photometer, 33 Violle's absolute standard, 163 Violle-Siemens standard, 169 Visual acuteuess, Photometers based on, 77 Voltaic arc, 224 Voltaic arc, The nature and appear- ance of the, 225 Weber's photometer, 85-305 Wheatstone's photometer, 100 Wild's polarization photometer, 69 Wybauw's compensation method, 72 Van Nostrand's Science Series IVmo, Fancy Boards, Profusely Illustrated. 5O Cents each. No. 39. Hand-Book Electro-Magnetic Telegraph ; by A. E. Loring. " 53. Induction Coils ; How Made and How Used. 57. Incandescent Electric Lights, with particular reference to the Edison New edition preparing. 64. Electro Magnets ; the Determination of the elements of their Con- struction ; by Comte DuMoncel. 66. Dynamo-Electric Machinery ; A Series of Lectures ; by Sylvanus P. Thompson, with an Introduction and Notes by F. L. Pope. 71. Dynamic Electricity ; Its Modern Use and Measurement chiefly in its application to Electric Lighting and Telegraphy, including I. Some Points in Electric Lighting ; by Dr. John Hop- kinson. II. On the Measurement of Electricity for Commercial Purposes ; by J. N. Shoolbred. HI. Electric Light Arithmetic ; by K E. Day. " 75. Becent Progress on Dynamo-Electric Machines, being a Supplement to Dynamo-Electric Machinery ; by S. P. Thompson. The Series now number 95 Volumes, and embrace Works on every Subject. NEW VOLUMES ON ELEOTEICAL SUBJECTS ARE IN PREPARATION. Complete List of the Series will be sent to any address on application. D. VAN NOSTRAND COMPANY 23 MURRAY AND 27 WARREN STREETS, NEW YORK AND ITS APPLICATION BY THE ELECTRIC MOTOR, Including Electric Railway Construction, By PHILIP ATKINSON, A. M. Ph. D. Author of "Elements of Static Electricity" "The Elements of Electric Lighting" and "The Elements of Dynamic Electricity and Magnetism" 244 Pages, 12mo., 96 Illustrations, Price, $2.00. A Full, Clear Description of the Electric Motor, in its Latest Construction, both for the Direct and Alternating Current, and its Various Applications, in a plain style, free from tech- nicality and mathematical formulae, and adapted to the comprehension of every one; show- ing how power is electrically transformed and transmitted. CONTENTS. CHAPTER I. DEFINITIONS. The Conservation of Energy. Electric Terms. Potential. Electromotive Force. Resistance. Current. Ohm's Law. Induction. C. G. S. Units. The Dyne. The Erg. Electric Units. The Volt. The Ohm. The Ampere. The Watt. The Electric Horse-Power. Table of Dimensions and Resistances of Pure copper Wire. CHAPTER II. PRINCIPLES OF THE ELECTRIC MOTOR. The Motor a Means of Applying Power. Sources of Electric Energy. Classification of M otors. Construction of Direct Current Motors. TheArmatuie. The commutator. The Brushes. The Field-Magnets. The Series Wound Motor. The Shunt Wound Motor. Operation of the Motor as a Dynamo, commutation. Polarity and Neutral Line. Coreless Construction. Reversal of Rotation. Position of the Brushes. Operation of the Direct Current Motor. Effect of Current Reversal on Rotation. Polar Rotation. Counter Electromotive Force. Position of the Poles and Neutral Line. Eddy Currents. Loss of Power. Series and Shunt Motors compared, constant Current and Con- stant Potential Circuits and Motors. The Rheostat. Rheostat Connections. Electric Heat and Mechanical Energy. Motor Designing. CHAPTER III. STATIONARY MOTORS. The Excelsior Motor. The Edison Standard Motor. The Edison Small Motor. The C. & C. Standard Motor. The C. & C. Small Motors. The Detroit Motor. The Eddy Motor. The Perret Motor. Alternating Current Motors. The Tesla Alternating Current Motor. The Stanley Kelly Alternating Current Motor. Single Phase Alternating Current Motors. The Brown Single Phase Alterna- ting Current Motor. CHAPTER IV. APPLICATIONS OF THE STATIONARY MOTOR. General Remarks. Electric Fans and Ven- tilators Electric Operation of Pipe Organs. Electric Elevators. The Otis Electric Elevator. The yprague- Pratt Electric Elevator. Electric Dock Hoists. Electric Traveling Cranes. Electric Operation of Printing Presses, commercial M easurement of Electric Energy. Electric Operation of Dental Apparatus. Electric Operation of Medical and Surgical Apparatus. Electric Operation of ship Drills. The tdlson Electric Per- cussion Drill. The Van Depoele Electric Percussion Drill. The Electric Diamond Drill. The Triplex Electric Pump. The Sperry Pick Electric Coal Cutter. The New Arc Electric Coal Cutter. Various Electric Mining Apparatus. CHAPTER V. ELECTRIC RAILWAYS AND RAILWAY MOTORS. General Remarks. Line Construction. Feeders. Poles. Trolleys. The Boston Trolley. The Emmet Trolley. The Compression Spring Trolley. The Siemens-Halske Sliding Contact. The Tube and Piston Contact. The Double Trolley. Insulators and Clamps. Switches. Three-Way Switch. The Emmet Switch. The Atkinson Switch. Right- Angled Cross- Ing. The Ramsay Adjustable Crossing. Trolley Line-Breaker. The Johnston Disconnector. Railway Mo- tors. The Westinghouse Single Reduction Motor. Controller. Controller Connections. Lightning Arrester. The Thomson-Houston Water-Proof Single Reduction Motor. The Curtis Single Reduction Motor. Gearless Motors. The Short Gearless Motor. Electric Lighting of the Cars. Electric Heating of the Cai s. The Bur- ton Electric Heater. The Conduit System. The Siemens-Halske Conduit Railway. The Love Conduit Railway. Closed Conduits. The Wheless Conduit Railway. Elevated and Underground Electric Railways. The Liverpool Elevated Electric Railway. The City and South London Underground Electric Railway. Storage Batteiy Traction. Electric Haulage in Mines. Electric Haulage in Mills and Factories. CHAPTER VI. CENTRAL STATION CONSTRUCTION AND EQUIPMENT. Development of the Central Station. Chicago Edison Central Station No. l. Chicago Edison Central Station No. 5. Cicero and Proviso Street Railway Central Station. Waterpower Stations and Long Distance Transmission. The Frankfort-Lauffen Experiment. Willamette Falls Waterpower Station. Tellurlde Waterpower station. Direct connected Dynamos. D. VAN NOSTRAND COMPANY, PUBLISHERS, V Copies sent by mail on receipt of price. 23 Murray & 27 Warren Sts. f New York ALTERNATE CURRENT TRANSFORMER, . IN THEORY AND PRACTICE, By J. A. FLEMING, M. A., D. Sc. (Lond.). Professor of Electrical Engineering in University College, London ; Fellow and late Scholar of St. John's Col- lege, Cambridge ; Fellow of University College, London; Member of the Institution of Electrical Engin- eers ; Member of the Physical Society of London ; Member of the Royal Institution of Great Britain, &c. (IN TWO Vol. I.-THE INDUCTION OF ELECTRIC CURRENTS. 487 Pages, 8vo, fully Illustrated. Price, $3.00. -**~m-* EXTRACT FROM PREFACE. The present treatise la an attempt to place before the reader an elementary account of the principles which underlie the operations and the use of the Alternating-Current Transformer. It frequently hap- pens that whilst practical students are in possession of clear ideas on the fundamental phenomena exhibited In the application and generation of continuous or steady electric currents, the endeavor to cope with simi- lar problems concerning periodic currents finds them in want of some special assistance to enable them to deal with the peculiar difficulties which surround such study. Particularly is this the case now that periodic or alternating currents are largely employed in electric illumination, and the necessity arises for all students of electro-technics to be prepared to deal with and appreciate the particular questions which thus arise. The prr.ctical employment of periodic currents and their inductive transformation is becoming so important that it seemed probable service would be rendered to those dealing with these matters by placing together the main outlines of the theory and of the applications of electro-current induction. The work here presented is an attempt to realize this aim. In the first volume the General Phenomena and Effects of Electric- Current Induction, Periodic Currents, and Electro-Magnetic Induction are considered, together with so much collat- eral matter as is necessary to a clear comprehension of the subject. In the second volume it is proposed to consider the subjects of Practical Measurements, the Construction, Design, and use of Induction Transfor- mers, and the applications in Lighting, Welding, and other Technical Work. CONTENTS. CHAPTER I. Introductory. CHAP. II. Electro-Magnetic Induction. CHAP. III. The Theory of Simple Periodic Currents. CHAP. IV. Mutual and Self Induction. CHAP. V, Dynamical Theory of Current Induction. Vol. II.-THE UTILIZATION OF INDUCED CURRENTS. 594 Pages, 312 Illustrations, 8vo, cloth, Price, $5,00, CONTENTS. CHAPTER 1. The Historical Development of the Induction Coil and Transformer. CHAP. II. The Distribution of Electrical Energy by Transformers. CHAP. III. Alternate- Current Electric Stations. CHAP. IV. The Construction and Action of Transformers. CHAP. V. Other Practical Uses of Transformers. D. VAN NOSTRAND COMPANY, Publishers, 23 Murray and 27 Warren Streets, * # * Copies Bent by mail on receipt of price. N E W YO R K. IN PRESS. A MANUAL FOR THE DESIGN OF ELECTRICAL CIRCUITS. ARTHUR VAUGHAN ABBOTT, C. E. Chief Engineer Chicago Telephone Company, Member A merican Society Electrical En- gineers, Member American institute of Mining Engineer -s, Junior American Society of Civil Engineers. The conducting circuit of transmission plants lias, as yet, only received in- cidental treatment in connection with general descriptions of installations for the production and utilization of electrical energy. It is the purpose of the pre- sent manual to deal exclusively with the conducting circuit, giving such an ac- count of the materials commonly used for electrical circuits and their disposition, as will enable the designer to accurately and economically plan a conducting circuit for any desired plant. CHAPTER I. DISTRIBUTION IN GENERAL. Distribution in series Distribution in parallel Mixed systems Indirect Distribution. II. ELECTRICAL CONDUCTORS AND INSULATORS. III. THE HEATING OF CONDUCTORS. IV. THE PROPERTIES OF WIRE. V. THE CONSTRUCTION OF AERIAL CIRCUITS. Part 1. General Line Work. Part 2. Electric Railway Circuits. Part 3. Lightning Arresters. *' VI. CONDUIT AND CONDUIT CONDUCTORS. Part 1. Conduits. Part 2. Cables and Conduit Conduct- ors. VII. ELECTRICAL INSTRUMENTS. " VIII. METHODS OF MEASUREMENT. IX. SERIES DISTRIBUTION. X. DISTRIBUTION IN PARALLEL. XI. MISCELLANEOUS METHODS. XII. THE COST OF PLANT CONSTRUCTION, AND COST OF PRODUCTION OF POWER. D. VAN NOSTRAND CO., Publishers ..Copies sent by mail on receipt of price. 23 Murray & 27 Warren StS., New York. IN PRESS. 1 Vol. Quarto. 125 Full-Page Plates, 60 Tables and Descriptive Letter-Press. BY H. F. PARSHALL, Consulting Designing Engineer of the General Electric Compiny ; Member of American Society of Mechanical Engineers, and American Institute Electrical Engineers^ AND H. M. HOBART, S. B. The treatise discusses exhaustively the principles governing the arrange- ment of armature conductors of electrical machines, both continuous and alter- nating current, including various multiphase windings applicable in practice. The plan of each chapter is first, a general discussion of the properties of the windings treated, the explanation of the formulae applicable, illustrated by diagrams showing each useful form of winding. The treatment is so complete that windings can be designed from the information given in the chapters, but in addition to this there are given 60 tables showing exactly how, with a given number of conductors, the windings have to be arranged for a given result. These tables eliminate the necessity for special calculations, so that those un- certain in the use of figures may be able to design armature windings with accuracy. OOltfTEHXTTS CHAPTER I. SINGLE- WOUND GRAMME RINGS. II. DOUBLE-WOUND GKAMME RlNGS. III. Two-CiKouiT, SINGLE- WOUND MULTIPOLAR RINGS. IV. TWO-CIRCUIT, MULTIPLE-WOUND MULTIPOLAR RINGS. V. BIPOLAR DRUM WINDINGS. VI. MULTIPLE-CIRCUIT, SINGLE-WOUND, MULTIPOLAR DRFMS. VII. MULTIPLE-CIRCUIT, MULTIPLE-WOUND, MULTIPOLAR DRUMS. VIII. TWO-CIRCUIT, SINGLE-WOUND, DRUMS. IX. INTERPOLATION OF COMMUTATOR SEGMENTS. X. TwO-ClROUIT, MULTIPLE-WOUND DRUM ARMATURES. XL RULES AND TABLES CONTINUOUS CURRENT WINDINGS. XII SINGLE-PHASE, ALTERNATING CURRENT WINDINGS. XIII QUARTER-PHASE ALTERNATING CURRENT WINDINGS. XIV. TiiREE-PiiASK ALTERNATING CURRENT WINDINGS. D.VAN NOSTRAND COMPANY, Publishers, Importers & Booksellers of Scientific Books, 23 MURRAY AND 27 WARREN STREETS, NKW YORK. RETURN TO * ENGINEERING LIBRARY .642-3366 LOAN PERIOD 1 2 3 4 5 6 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS Overdues subject to replacement charges DUE AS STAMPED BELOW JUn 2 81991 UNIVERSITY OF CALIFORNIA, BERKELEY FORM NO. DD1 1 , 80m, 8/80 BERKELEY, CA 94720 U.C. BERKELEY LIBRARIES CD2M33M8T8 <- HI