PHYSICS DEPT. UNIVERSITY OF CALIFORNIA LIBRARY OF THE DEPARTMENT OF PHYSICS Received Accessions No. ./QQ& Book No ...... /. f y SOME CONTRIBUTIONS FROM THE LABORATORY OF PHYSICS OF THE UNIVERSITY OF ILLINOIS o URBANA, ILLINOIS for 1914-1919 In Two Parts PART I PHYSICS oirr. SOME CONTRIBUTIONS FROM THE LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS for 1914-1919 Parti TABLE OF CONTENTS Acoustics of Auditoriums. Bulletin of the Engineering Experiment Sta- tion, University of Illinois, March, 1914. F. R. Watson ' A Modified Method of Measuring e/m and v for Cathode Rays. Re- printed from the Physical Review, May, 1914. L. T. Jones The Determination of e/m for Cathode Rays as a Laboratory Experiment for an Undergraduate Course in Electrical Measurements. Re- printed from School Science and Mathematics, October, 1914. C. T. Knipp An Attempt at an Electromagnetic Emission Theory of Light. Reprinted from the Physical Review, June, 1914. J. Kunz Some Brush Discharge Phenomena Produced by Continuous Potentials. Reprinted from the Physical Review, July, 1914. S. P. Farwell The Diffusion of Gases at Low Pressures Made Visible by Color Effects. Reprinted from Science, July 16, 1915. C. T. Knipp On the Present Theory of Magnetism. Reprinted from the Physical Re- view, August, 1915. J. Kunz The Absorption of Air by Charcoal Cooled to the Temperature of Liquid Air. Reprinted from Science, September, 1915. f~* T 1 T7" L. 1 . Knipp Acoustics of Auditoriums. Reprinted from The Brickbuilder, October, 1915. F. R. Watson Saturation Value of the Intensity of Magnetization and the Theory of the Hysteresis Loop. Reprinted from the Phys'cal Review, Novem- ber, 1915. E. H. Williams Color Effects of Positive and of Cathode Rays in Residual Air, Hydrogen, Helium, etc. Reprinted from Science, December 31, 1915. C. T. Knipp The Structure of T Rays on the Basis of the Electro-Magnetic Theory of Light. Reprinted from the Physical Review, December, 1915. J. Kunz On the Construction of Sensitive Photoelectric Cells. Reprinted from the Physical Review, January, 1916. J. Kunz and J. Stebbins An Investigation of the Transmission, Reflection and Absorption of Sound by Different Materials. Reprinted from the Physical Review, Jan- uary, 1916. F. R. Watson 3 A Study of Ripple Wave Motion. Reprinted from the Physical Review, February, 1916. F. R. Watson and W. A. Shewhart Photographs Showing the Relative Deflection of the Positive and of the Negative Ions as Compared with that of the Electron. Reprinted from Science, March 17, 1916. C. T. Knipp Electrical Discharge Between Concentric Cylindrical Electrodes. Re- printed from Science, June 2, 1916. C. T. Knipp Retrograde Rays from the Cold Cathode. Reprinted from the Physical Review, June, 1916. O. H. Smith An Experimental Verification of the Law of Variation of Mass with Ve- locity for Cathode Rays. Reprinted from the Physical Review, July, 1916. L. T. Jones On the Initial Condition of the Corona Discharge. Reprinted from the Physical Review, July, 1916. J. Kunz Determination of the Laws Relating lonization Pressure to the Current in the Corona of Constant Potentials. Reprinted from the Physical Review, September, 1916. E. H. Warner Direct Current Corona from Different Surfaces and Metals. Reprinted from the Physical Review, October, 1916. S. J. Crooker To Cut Off Large Tubes of Pyrex Glass. Reprinted from Science, May 9, 1919. C. T. Knipp Tolman's Transformation Equations, the Photoelectric Effect and Radi- ation Pressure. Reprinted from the Physical Review, March, 1917. S. Karrer An Improved High Vacuum Mercury Vapor Pump. Reprinted from the Physical Review, March, 1917. C. T. Knipp A Simple Demonstration Tube for Exhibiting the Mercury Hammer, Glow by Mercury Friction, and the Vaporization of Mercury at Reduced Pressure. Reprinted from School Science and Mathematics, May, 1917. C. T. Knipp Distribution of Potential in a Corona Tube. Reprinted from the Physical Review, September, 1917. H. T. Booth The Pressure Increase in the Corona. Reprinted from the Physical Re- view, November, 1917. E. H. Warner On Bohr's Atom and Magnetism. Reprinted from the Physical Review, July, 1918. J. Kunz The Magnetic Properties of Some Rare Earth Oxides as a Function of the Temperature. Reprinted from the Physical Review, August, 1918. E.H.Williams Amplification of the Photoelectric Current by Means of the Audion. Re- printed from the Physical Review, February, 1919. C. E. Pike UNIVERSITY OF ILLINOIS ENGINEERING EXPERIMENT STATION BULLETIN No. 73 MARCH, 1914 ACOUSTICS OF AUDITORIUMS. BY F. R. WATSON, ASSISTANT PROFESSOR OF PHYSICS. CONTENTS. p ag e I. Introduction 3 Acknowledgment 5 II. Behavior of Sound Waves in a Room 5 III. Methods of Improving Faulty Acoustics 8 A. Reverberation and Its Cure 8 Experimental Work on Cure of Reverberation 9 Formulae for Reverberation of Sound in a Room 10 B. Echoes and Their Remedy 11 C. Popular Conception of Cures. Use of Wires and Sound- ing Boards 11 Sounding Boards 12 Modeling New Auditorium after Old Ones with Good Acoustics 12 D. The Effect of the Ventilation System on the Acoustics. .. 13 IV. The Investigation in the Auditorium at the University of Illinois 13 A. Preliminary Work 13 B. Details of the Acoustical Survey in the Auditorium 17 C. Conclusion Drawn from the Acoustical Survey 26 D. Methods Employed to Improve the Acoustics 26 Reflecting Boards 26 Sabine's Method 26 Method of Eliminating Echoes 29 Proposed Final Cure. , 29 V. Bibliography of Publications on Acoustics of Auditoriums. . . 31 ACOUSTICS OF AUDITORIUMS AN INVESTIGATION OF THE ACOUSTICAL PROPERTIES OF THE AUDITORIUM AT THE UNIVERSITY OF ILLINOIS. I. INTRODUCTION. Much concern has arisen . 1913. 4. Sabine and Watson. Ibid. 14 ILLINOIS ENGINEERING EXPERIMENT STATION The attempt to locate echoes by generating a sound and listening with the ear met with only partial success. The ear is sensitive enough, but becomes confused when many echoes are present, coming apparently from every direction, so that the evidence thus obtained is not altogether conclusive. It became apparent that the successful solution lay in fixing the attention on the sound going in a particular direction -and finding out where it went after reflection ; then tracing out the path in another particular direction, and so on, until the evidence obtained gave some hint of the general action of the sound. > FIG. 4. WATCH AS SOURCE OF SOUND, BACKED BY A CONCAVE REFLECTOR. The first step in the application of this principle was to use a faint sound which could not be heard at any great distance unless rein- forced in some way. The ticks of a watch were directed, by means of a reflector (Fig. 4) to certain walls suspected of giving echoes. Using the relation that the angle of incidence equals the angle of reflection, the reflected sound was readily located, and the watch ticks heard dis- tinctly after they had traveled a total distance as great as 70 to 80 feet from the source. In a later experiment, a metronome was used which gave a louder sound. It was enclosed in a sound-proof structure (Fig. 5) with only one opening, so that the sound could be directed by means of a horn. This method was suggested by the work of Gustav Lyon in the Hall of the Trocadero at Paris,* where a somewhat similar arrangement was used. The method was successful and verified the observations taken previously. r La Nature (Paris), April 24, 1909. WATSON ACOUSTICS OF AUDITORIUMS SOUND PROOF BOX 15 FIG. 5. METRONOME AS SOURCE OF SOUND. Though the results obtained with the watch and metronome seemed conclusive, yet the observer was not always confident of the results. A further method was sought, and a more satisfactory one found by using an alternating current arc-light at the focus of a parabolic re- flector (Fig. 6). In addition to the light, the arc gave forth a hissing sound, which was of short wave length and therefore experienced but little diffraction. The bundle of light rays was, therefore, accompanied by a bundle of sound, both coming from the same source and subject. FIG. 6. ARC-LIGHT AS SOURCE OF SOUND. to the same law of reflection. The path of the sound was easily found by noting the position of the spot of light on the wall. The reflected sound was located by applying the relation that the angles of inci- dence and reflection are equal. The arc-light sound was intense and gave the observer confidence in results that was lacking in the other 16 ILLINOIS ENGINEERING EXPERIMENT STATION methods. To trace succcessive reflections, small mirrors were fastened to the reflecting walls so that the path of the reflected sound was indi- cated by the reflected light. A "diagnosis" of the acoustical troubles of the Auditorium was then made by this method. It should be noted here that the arc-light sound is not the same as the sounds of music or speech, these latter ones being of lower pitch and of longer wave length. It was, therefore, a matter of doubt whether the results obtained would hold also for the case of speech or music. Tests made by observers stationed in the Auditorium when musical num- bers and speeches were rendered, however, verified the general conclusions obtained with the arc-light. It should be pointed out in this connection that there is an objection to applying the "ray" method of geometrical optics to the case of sound. It is much more difficult to get a ray of sound than it is to get a ray of light.* This is due to the difference in the wave lengths in the two cases. It appears that the waves are diffracted, or spread out, in propor- tion to their length, the longer waves being spread out to a greater extent. The short waves of light from the sun, for instance, as they come through a window mark out a sharp pattern on the floor, which shows that the waves proceed in straight lines with but little diffraction or spreading. Far different is it with the longer waves of sound. If the window is open, we are able to hear practically all the sounds from outdoors, even that of a wagon around the corner, although we may be at the other end of the room away from the window. The longer sound waves spread out and bend at right angles around corners, so that it is almost impossible to get a sound shadow with them. Furthermore, in the matter of reflection, it appears that the area of the reflecting wall must be comparable with the length of the waves being reflected. In the case of light, the waves are very minute, hence a mirror can be very small and yet be able to set up a reflection ; but sound waves are of greater 1-ength, the average wave length of speech (45 cm.) being about 700000 times longer than the wave length of yellow light (.00006 cm.), hence the reflecting surface must be correspondingly larger. An illustration will perhaps make this clearer. Suppose a post one foot square projects through a water surface. The small ripples on the water will be reflected easily from the post, but the large water waves pass by almost as if the post were not there. The reflecting surface must have an area com- parable with the size of the wave if it is to cause an effective reflection. Eelief work in auditoriums, if of small dimensions, will affect only the high pitched sounds, i. e., those of short wave length, while the low *Rayleigh, "Theory of Sound," Vol. II, 283. WATSON ACOUSTICS OF AUDITORIUMS 17 pitched sounds of long wave length are reflected much the same as from a rather rough wall. It is also shown that the area of the reflecting surface is dependent on its distance from the source of sound and from the observer ; the greater these distances are the larger must be the reflecting surface.* These considerations all show that the reflection of sound is a com- plicated matter. The dimensions of a wall to reflect sound, or of relief work to scatter it, are determined by the wave length and by the various other factors mentioned. It should be said with caution that a "ray" of sound is reflected in a definite way from a small bit of relief work. We must deal with bundles of sound, not too sharply bounded, and have them strike surfaces of considerable area in order to produce reflections with any completeness. FIG. 7. LONGITUDINAL SECTION SHOWING THE CHIEF CONCENTRATIONS OF SOUND, THE DIFFRACTION EFFECTS BEING DISREGARDED. B. DETAILS OF THE ACOUSTICAL SURVEY IN THE AUDITORIUM. The general effect of the walls of the Auditorium on the sound may be anticipated by considering analogous cases in geometrical optics, but with the restrictions on "rays" described in the preceding paragraph. The sound does not actually confine itself to the sharp boundaries shown. The diagrams are intended to indicate the main effect of the sound in the region so bounded. Pig. 7 gives such an idea for the concentration of sound in the longitudinal section of the Auditorium. *Rayleigh, ibid., 283. 18 ILLINOIS ENGINEERING EXPERIMENT STATION The plan followed in the experimental work was to anticipate the path of the sound as indicated in Fig. 7, then to verify the results with the arc-light reflector. Figs. 8 and 9 show the effect of the rear wall in the balcony in forming echoes on the stage. The speaker was particu- larly unfortunate,, being afflicted with no less than ten echoes. FIG. 8. LONGITUDINAL SECTION SHOWING How SOUND Is STAGE TO FORM AN ECHO. RETURNED TO THE FIG, 9. LONGITUDINAL SECTION SHOWING FORMATION OF ECHO ON THE STAGE. The hard, smooth, circular wall bounding the main door under the balcony gave echoes as shown in Fig. 10, the sound going also in the reverse direction of the arrows. WATSON ACOUSTICS OF AUDITORIUMS Vk L ~- ^ 19 FIG. 10. PLAN OF AUDITORIUM SHOWING ACTION OF REAR WALL ON THE SOUND. FLOOR. PLAN FIG. 11. PLAN OF AUDITORIUM SHOWING CONCENTRATION OF SOUND BY THE REAR WALL. ILLINOIS ENGINEERING EXPERIMENT STATION FlG. 12. THIS FIGURE TAKEN WITH FIG. 9 SHOWS How AN ECHO Is SET UP ON THE STAGE. A more comprehensive idea of the action of this wall is shown in Fig. 11. This reflected sound was small in amount and therefore not a serious disadvantage. The cases cited were fairly easy to determine since the bundles of sound considered were confined closely to either a vertical or a horizontal plane for which the plans of the building gave some idea of the probable path of the sound. For other planes, the paths followed could be antici- pated by analogy from the results already found. Fig. 12 shows in perspective the development of the result expressed in Fig. 9. A square bundle of sound starts from the stage and strikes the spherical surface of the dome. After reflection, it is brought to a point focus, as shown, and spreads out until it strikes the vertical cylindrical wall in the rear of the balcony. This wall reflects it to a line focus, after which it proceeds to the stage. Auditors on all parts of the stage complained of hearing echoes. WATSON ACOUSTICS OF AUDITORIUMS 21 Referring to Fig. 7, it is seen that the arch over the stage reflects sound back to the stage. Fig. 13 shows in perspective the focusing action of this overhead arch. Fig. 14 shows the effect of the second arch. FIG. 13. PERSPECTIVE OF STAGE SHOWING FOCUSING ACTION OF ARCH ON SOUND. Some of this sound is reflected to the stage and to the seats in front of the stage ; other portions, striking more nearly horizontally, are reflected to the side balconies. The echoes are not strong except for high pitched notes with short wave lengths, since the width of the arch is small. Passing now to the transverse section, Fig. 15, we find the most pronounced echoes in the Auditorium. If an observer generates a sound in the middle of the room directly under the center of the skylight, distinct echoes are set up. A bundle of sound passes to the concave sur- face which converges the sound to a focus, after which it spreads out again to the other concave surface and is again converged to a focus ILLINOIS ENGINEERING EXPERIMENT STATION FIG. 14. PERSPECTIVE OF STAGE SHOWING FOCUSING ACTION OF SECOND ARCH. FIG. 15. TRANSVERSE SECTION SHOWING HOW MOST PRONOUNCED ECHOES ARE SET UP BY THE Two CONCAVE SURFACES. WATSON ACOUSTICS OF AUDITORIUMS 23 nearly at the starting point. The distance traveled is about 225 feet, taking about *4 second, so that the conditions are right for setting up a strong echo. This echo is duplicated by the sound which goes in the reverse of the path just described. Another echo, somewhat less strong, is formed by the sound that goes to the dome overhead and which is reflected almost straight back, since the observer is nearly at the center of the sphere of which the dome is a part. These echoes repeat them- selves, for the sound does not stop on reaching the starting point, but is reflected from the floor and repeats the action just described. As many as ten distinct echoes have been generated by a single impulse of sound. FIG. 16. ACTION OF SOUND IN CAUSING ECHO ON THE STAGE. The echo shown in Fig. 15 is repeated in a somewhat modified form for a sound generated on the stage by a speaker. Fig. 16 shows the path taken by the sound. This echo is duplicated by the sound that goes in the reverse direction of the arrows, so the speaker is greeted from 24 ILLINOIS ENGINEERING EXPERIMENT STATION both sides. Fig. 17 is a perspective showing the path. The sound does not confine itself closely to a geometrical pattern,, as shown in the picture, but spreads out by diffraction. The main effect is shown by the figure. FIG. 17. PERSPECTIVE SHOWING HOW AN ECHO Is FORMED ON THE STAGE BY Two REFLECTIONS. DIFFRACTION EFFECTS ARE NOT CONSIDERED IN THIS DRAWING. Thus far only the echoes that reached the stage have been described. Other echoes were found in other parts of the hall, and it seemed that few places were free from them. The side walls in the balcony, for instance, were instrumental in causing strong echoes in the rear of the balcony. Fig. 18 shows in perspective the action of one of these walls. These two surfaces were similar in shape and symmetrically placed. Each was the upper portion of a concave surface with its center of curvature in the center of the building under the dome. The general effect of the left hand wall was to concentrate the sound falling on it WATSON ACOUSTICS OE AUDITORIUMS 25 in the right hand seats in the balcony. Some of the sound struck the opposite wall and was reflected to the stage, as shown in Fig. 17. Audi- tors who sought the furthermost rear seats in the balcony to escape echoes were thus caught by this unexpected action of the sound. The right hand wall acted in a similar way to send the sound to the upper left balcony. FIG. 18. PERSPECTIVE SHOWING SOUND REFLECTOR FROM CONCAVE WALL IN BALCONY. DIFFRACTION NOT CONSIDERED. The dome surface concentrates most of its sound near the front of the central portion of the balcony and the ground floor in front of the .balcony in the form of a caustic cone. Figs. 7, 9 and 11 give some conception of how a concentration of sound is caused by this spherical surface. The echo in the front portion of the balcony was especially distinct. On one occasion, in this place, the author was able to hear the speaker more clearly torn the echo than by listening to the direct sound. 26 ILLINOIS ENGINEERING EXPERIMENT STATION Minor echoes were set up by the horizontal arch surfaces in the balcony. The sound from the stage was concentrated by reflection from these surfaces and then passed to a second reflection from the concave surfaces back of them. Auditors in the side balcon} r were thus disagree- ably startled by having the sound come from overhead from the rear. C. CONCLUSION DRAWN FROM THE ACOUSTICAL SURVEY. The results of the survey show that curved walls are largely respon- sible for the formation of echoes because they concentrate the reflected sound. It seems desirable, therefore, to emphasize the danger of using such walls unless their action is annulled by absorbing materials or relief work. Large halls with curved walls are almost sure to have acoustical defects. D. METHODS EMPLOYED TO IMPROVE THE ACOUSTICS. Reflecting Boards. The provisional cure was brought about grad- ually by trying different devices suggested by the diagnosis. In one set of experiments sounding boards of various shapes and sizes were used. A flat board about five feet square placed at an incline over the position of the speaker produced little effect A larger canvas surface, about 12 by 20 feet, was not much better. A parabolic reflector, however, gave a pronounced effect. This reflector was mounted over a pulpit at one end of the stage and served to intercept much of the sound that otherwise would have gone to the dome and produced echoes. The path of the reflected sound was parallel to the axis of the paraboloid of which the reflector was a quarter section. There was no difficulty in tracing out the reflected sound. Auditors in the path of the reflected rays reported an echo, but auditors in other parts of the Auditorium were remarkably free from the usual troubles. The device was not used permanently, since many speakers objected to the raised platform. More- over, it was not a complete cure, since it was not suited for band con- certs and other events, where the entire stage was used. Another reflector similar in shape to the one just described is shown in Figs. 21 and 22. Sabine's Method. The time of reverberation was determined by Sabine's method. An organ pipe making approximately 526 vibrations a second was blown for about three seconds and then stopped. An auditor listened to the decreasing sound, and when it died out made a record electrically on a chronograph drum. The time of reverberation was found to be 5.90 seconds, this being the mean of 19 sets of measure- ments, each of about 20 observations. The reverberation was found also by calculation from Sabine's equation (see Section III), taking the volume of the Auditorium as 11 800 cubic meters and calculating the WATSON ACOUSTICS OF AUDITORIUMS FIG. 19. REFLECTING BOARD IN PROCESS OF CONSTRUCTION. FIG. 20. FINISHED REFLECTOR. HARD PLASTER ON WIRE LATH. ILLINOIS ENGINEERING EXPERIMENT STATION FIG. 21. PARABOLIC REFLECTOR SHOWING ITS ACTION ON SOUND. FIG. 22. PHOTOGRAPH OF PARABOLIC REFLECTOR. WATSON ACOUSTICS OF AUDITORIUMS 29 absorbing power of all the surfaces in the room. This calculation gave 6.4 seconds. The agreement between the two results is as close as could be expected, since neither the intensity of the sound nor the pitch used by the author was the same as those used by Professor Sabine, and both of these factors affect the time of reverberation. Several years later the time of reverberation was again determined after certain changes had been made. A thick carpet had been placed on the stage, heavy velour curtains 18 by 32 feet in area hung on the wall at the rear of the stage, a large canvas painting 400 square feet in area was installed, and the glass removed from the skylight in the ceiling. The time of reverberation was reduced to 4.8 seconds. With an audience present this value was reduced still more, and when the hall was crowded at commencement time the reverberation was not troublesome. Method of Eliminating Echoes. Although the time of reverberation was reduced to be fairly satisfactory, as just explained, the echoes still persisted, and were very annoying. Attempts were made to reduce individual echoes by hanging cotton flannel on the walls at critical points. Thus the shaded areas in Fig. 17 were covered and also the entire rear wall in the balcony. Pronounced echoes still remained, and it was evident that some drastic action was necessary to alleviate this condition. Four large canvases, shown in Figs. 23 and 24, were then hung in the dome in position suggested by the results of the diagnosis. A very decided improvement followed. For the first time the echoes were reduced to a marked degree and speakers on the stage could talk without the usual annoyance. This arrangement eliminated the echoes not only on the stage, but generally all over the house. A number of minor echoes were still left, but the conditions were much improved, especially when a large audience was present to reduce the reverberation. Proposed Final Cure. The state of affairs just described is the condition at the time of writing. Two propositions were considered in planning the final cure. One proposition involved a complete remodeling of the interior of the Auditorium. Plans of an interior were drawn in accordance with the results of the experimental work that would probably give satisfactory acoustics. This proposition was not carried out because of the expense and because it was thought desirable to attempt a cure without changing the shape of the room. The latter plan is the one now being followed. It is proposed to replace the present unsightly curtains with materials which will conform to the architectural features of the Auditorium and which will have a pleasing color scheme. At the same time, it will be necessary to hold to the features which have improved the acoustics. 30 ILLINOIS ENGINEERING EXPERIMENT STATION FIG. 23. PHOTOGRAPH OF Two OF THE CANVAS CURTAINS IN THE DOME OF THE AUDITORIUM. NOTE ALSO THE ABSORBING MATERIALS UNDER THE ARCHES. FIG. 24. PHOTOGRAPH OF DOME OF AUDITORIUM SHOWING THE CANVASES IN- STALLED TO ELIMINATE ECHOES. WATSON ACOUSTICS OF AUDITORIUMS 31 encyclopaedia of acoustics, the following topics applying to the subject in hand: "Akustik der Gebaude," pp. 580-584, with references. "Nachhall und Echo," pp. 565-569, with V. BIBLIOGRAPHY OF PUBLICATIONS ON ACOUSTICS OF AUDITORIUMS. Auerbach, F. "Akustik." Winkelmann's Handbuch der Physik, Vol. II, 1909. An " : "Akmtik with refer- ences. Blackall, C. H. "Acoustics of Audience Halls," Engineering Record, Vol. 45, pp. 541- 542, 1902. A paper recording the opinions of the author with many references to acoustical properties of particular audience halls. Cornelison, R. W. "The Acoustical Properties of Rooms Particularly as Affected by Wall Coverings," 1905. A pamphlet describing the merits of "Fabrikona" burlap as a sound absorber. H. B. Wiggin's Sons Company, Bloomfield, N. J. Eichhorn, A. "Die Akustik Grosser Raume nach Altgriechischer Theorie." Ernst and Korn, Publishers, Berlin, 1888. A discussion of Greek buildings and acoustics, with appli- cations to modern conditions. Eichhorn, A. "Der Akustische Masstab fur die Projectbearbeitung Grosser Innen Raume." Published by Schuster and Bufleb, Berlin, 1899. A continuation of the previous work. Exner, S. "Uber die Akustik von Horsalen und ein Instrument, sie zu bestimmen." Zeitschrift des Osterreichischen Ingenieur und Architekten-Vereines, Vol. LVII, p. 141, March, 1905. Indicates his opinion of good acoustical properties in a hail. Gives experi- mental determination of reverberation. Fournier, Lucien. "The Suppression of Echoes." La Nature (Paris), April 24, 1909. English translation given in "The Literary Digest," New York, May 29, 1909, p. 924. An account of the experiments of Gustav Lyon in investigating the echoes in Trocadero Hall in Paris. Franklin, W. S. "Derivation of Equation of Decaying Sound in a Room and Defini- tion of Open Window Equivalent of Absorbing Power." Physical Review, Vol. 16, pp. 372-374, 1903. A theoretical development of the formula found experimentally by Sabine. Haege. "Bemerkungen fiber Akvstik." Zeitschrift fur Baumesen, Vol. IX, pp. 582- 594, 1859. Henry, Joseph. "Acoustics Applied to Public Buildings," Smithsonian Report, 1856, p. 221. Hoyt, J. T. N. "The Acoustics of the Hill Memorial Hall," American Architect, Vol. CIV, pp. 50-53, August 6, 1913. Discusses the design of the hall and indicates how it ful- fills his ideas of good acoustics. Hutton, W. R. "Architectural Acoustics; Hall of Representatives, U. S. Capitol, 1858." Engineering Record, Vol. 42, p. 377, 1900. A discussion of the cure of the faulty acoustics in the U. S. Hall of Representatives. Jacques, W. W. "Effect of the Motion of the Air Within an Auditorium Upon Its Acoustical Qualities." Philosophical Magazine (5), Vol. 7, p. Ill, 1879. A record of experiments in the Baltimore Academy of Music showing that the ventilating current had a marked action on the acoustics. Jager, S. "Zur Theorie des Nachhals," Sitzungsberichten der Kaiserl. Akademie der Wissenschaften in Wien. Matem.-naturw. Klasse; Bd. CXX, Abt. Ha, Mai, 1911. An important paper giving a theoretical development of Sabine's formula showing the factors that enter into the constants. Considers also the case of the reflection of sound from a thin wall and also the case when it encounters a porous material such as a curtain. Lamb, Horace. "The Dynamical Theory of Sound." Published by Edward Arnold, London, 1910. A more elementary treatment than Rayleigh's "Theory of Sound." Marage. "Qualites acoustiques de certaines sailes pour la voix parlee." Comptes Rendus, Vol. 142, p. 878, 1906. An investigation of the acoustical properties of six halls in Paris. Norton, C. L. "Soundproof Partitions." Insurance Engineering, Vol. 4, p. 180, 1902. An account of experimental tests of the soundproof qu'alities of materials that are also fireproof. Orth, A. "Die Akustik Grosser Raume mit Speciallem Bezug auf Kirchen." Zeitschrift fur Bauwesen. Also reprint by Ernst and Korn, Berlin, 1872. Assumes that sound waves behave like light waves. Discusses, with detailed drawings, the paths of sound in the Zion Church in Berlin and the Nicolai Church in Potsdam. Also gives his opinion of the effect of surfaces and materials on sound. Rayleigh, Lord. "Theory of Sound." Two volumes, Macmillan, 1896. The unsur- passed classic in the subject of acoustics. References to architectural acoustics as follows: "Whispering Galleries," Vol. II, 287. "Passage of Sound Through Fabrics," Vol. II, p. 811. "Resonance in Buildings," Vol. II, 252. Sabine, Wallace C. "Architectural Acoustics." Engineering Record, 1900, Vol. 1, pp. 349, 876, 400, 426, 450, 477, 503. Published also in book form and in American Architect, Vol. 68, 1900, pp. 3, 19, 35, 43, 59, 75, 83. An important series of articles giving the relation between the time of reverberation in a room, the volume of the room, and absorb- ing materials present. Gives table of absorbing powers of substances, so that an archi- tect can calculate in advance of construction what the time of reverberation will be. 32 ILLINOIS ENGINEERING EXPERIMENT STATION Sabine, W. C. "Architectural Acoustics," Proc. of the Amer. Acad. of Arts and Sciences, Vol. XLII, No. 2, June, 1906. A continuation of the previous work, showing the accuracy of musical taste in regard to architectural acoustics and also the variation in reverberation with variation in pitch. Sabine, W. C. "Architectural Acoustics," Engineering Record, Vol. 61, pp. 779-781, June 18, 1910. Discusses the case of flow of air in a room and its effect on the acoustics. Con- cludes that the usual ventilation system in a hall has very little effect. Sabine, W. C. "Architectural Acoustics: The Correction of Acoustical Difficulties." The Architectural Quarterly of Harvard University, March, 1912, pp. 3-23. An account of the cures of the acoustical difficulties of a number of audience rooms, also a description of further experiments on the absorbing power of different materials. Sabine, W. C. "Theater Acoustics." American Architect, Vol. CIV, pp. 257-279, Decem- ber 31, 1913. Describes theater with model acoustics. Discusses behavior of sound in a room and shows photographs of sound waves in miniature rooms. Sabine, W. C. "Architectural Acoustics. Building Material and Musical Pitch." The Brickbuilder, Vol. 23, pp. 1-6, January, 1914. A continuation of previous work, describing absorbing powers of different materials. Sharpe, H. J. "Reflection of Sound at a Paraboloid." Camb. Phil. Soc. Proc., Vol. 15, pp. 190-197, 1909. Stewart, G. W. "Architectural Acoustics." Sibley Journal of Engineering, May, 1903. Published by Cornell University, Ithaca, N. Y. An account of an investigation leading to the cure of the acoustics of Sibley Auditorium. Sturmhofel, A. "Akustik des Baumeisters." Published by Schuster and Bufleb, Ber- lin, 1894. An 87-page pamphlet on the acoustics of rooms. Discusses effects of relief work in rooms on sound. Account of experimental work. References to auditoriums. Tallant, Hugh. "Hints on Architectural Acoustics." The Brickbuilder, Vol. 19, 1910, pp. Ill, 155, 199, 243, 265. A series of articles giving an exposition of the principles of the subject with practical applications. Tallant, Hugh. "Acoustical Design in the Hill Memorial Auditorium, University of Michigan." The Brickbuilder, Vol. XXII, p. 169, August, 1913. See also plates 113, 114, 115. A discussion of the acoustical results obtained in this auditorium, a special feature being the action of a huge parabolic reflecting wall surface over the stage. Tallant, Hugh. "Architectural Acoustics. The Effect of a Speaker's Voice in Different Directions." The Brickbuilder, Vol. 22, p. 225, October, 1913. Taylor, H. O. "A Direct Method of Finding the Value of Materials as Sound Ab- sorbers." Physical Review, Vol. 2 (2), p. 270, October, 1913. Tufts, F. L. "Transmission of Sound Through Porous Materials." Amer. Journal of Science, Vol. II, p. 357, 1901. Experimental work leading to the conclusion that sound is transmitted through porous materials in the same proportion that a current of air is. Watson, F. R. "Echoes in an Auditorium." Physical Review, Vol. 32, p. 231, 1911. An abstract giving an account of the experiments in the auditorium at the University of Illinois. Watson, F. R. "Inefficiency of Wires as a Means of Curing Defective Acoustics of Auditoriums." Science, Vol. 85, p. 833, 1912. Watson, F. R. "The Use of Sounding Boards in an Auditorium." Physical Review, Vol. 1 (2), p. 241, 1913. Also a more complete article in The Brickbuilder, June, 1913. Watson, F. R. "Air Currents and the Acoustics of Auditoriums." Engineering Record, Vol. 67, p. 265, 1913. A detailed account giving theory and experimental work, with application to ventilating systems in auditoriums. Watson, F. R. "Acoustical Effect of Fireproofed Cotton-Flannel Sound Absorbers." Engineering News, Vol. 71, p. 261, January 29, 1914. Results of experiments showing that cotton-flannel has practically the same absorbing power after fireproofing as before. Weisbach, F. "Versuche uber Schalldurchlassigkeit, Schallreflexion und Schallabsorb- tion." Annalen der Physik, Vol. 33, p. 763, 1910. Williams, W. M. "Echo in Albert Hall." Nature, Vol. 3, p. 469, 1870-71. Observa- tions on the shape of Albert Hall in London and the echoes set up. Editorial Notice. "The Dresden Laboratory for Architectural Acoustics." American Architect, Vol. 102, p. 137, October 16, 1912. States that a laboratory of applied acoustics is authorized in the Dresden (Germany) Technische Hochschule, and that expert advice will be furnished architects and others regarding problems of acoustics of auditoriums. PUBLICATIONS OF THE ENGINEERING EXPERIMENT STATION Bulletin No. I. Tests of Reinforced Concrete Beams, by Arthur N. Talbot. 1904. None available. Circular No. I. High Speed Tool Steels, by L. P. Breckenridge. 1905. None available. Bulletin No. 2. 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One dollar. Bulletin No. 72. Magnetic and Other Properties of Electrolytic Iron Melted in Vacuo, by Trygve D. Yensen. 1914. Forty cents. Bulletin No. 73. Acoustics of Auditoriums, by F. R. Watson. 1914. Twenty cents. *A limited number of copies of those bulletins which are starred are available for free distribution. [Reprinted from the PHYSICAL REVIEW, N.S., Vol. Ill, No. 5, May, 1914.] A MODIFIED METHOD OF MEASURING elm AND v FOR CATHODE RAYS. BY L. T. JONES. THIS determination of elm and v is a modification of the usual method employing the simultaneous electrostatic and magnetic deflections. The modification is the result of an attempt to eliminate as nearly as possible the errors of measurement of the deflections and the correction due to the field distribution at the ends of the electrostatic plates. This is brought about chiefly by the position in which the photographic plate was placed. THE APPARATUS. A glass cylinder 10 cm. in diameter and 27 cm. long (Fig. i) was closed at each end by a glass plate. Two holes were made in one of the plates to admit the glass tubes carrying the anode, A, and the cathode, C. The cathode, an alum- inum disc .6 cm. in diam- eter, was carried on an aluminum rod. This rod was encased in a small glass tube which in turn was supported by a larger glass tube waxed to the glass plate where it entered the discharge chamber. The anode was mounted in a similar manner. Both aluminum rods were connected with the outside by platinum wires sealed in glass. A brass ring, D, was fastened by sealing wax to the inside of the glass cylinder, and to this were fastened the soft iron shield, S, and the ebonite disc, B, the latter supporting the electrostatic plates. The electrostatic plates were held to the disc B by brass screws. The potential of the electrostatic plates was supplied through two wires that passed through small holes in the walls of the cylinder. The holes were sealed with wax. 317 Fig. 1. 3 l8 L. T.JONES. By loosening the screws holding the ebonite disc, B, to the brass ring, D, the disc and electrostatic plates could be taken as a whole from the cylinder. At the opposite end a short length of brass cylinder, G, was waxed to the inside of the glass cylinder and a hard rubber disc, F, turned to fit it, darkened the tube. The glass cylinder was coated on the outside with lamp black and the coating connected to earth. All the metal parts inside the tube, except the electrostatic plates and the discharge terminals, were connected to earth. THE ELECTROSTATIC PLATES. Two electrostatic plates were mounted exactly i cm. apart, as shown in Fig. 2. The beam of cathode rays was made to pass along the upper x^" of the two plates at grazing I incidence. The photographic J plate was placed flat on the . r\ lower of the two electrostatic plates. The beam was bent downward, by adjusting the Fig. 2. electric field, to strike the photographic plate well with- in the geometrical limits of the field plates. The cathode beam emerged from the Thomson plate-tube at a distance of several centimeters from the left end of the electrostatic plates and was then bent downward. Since the plates were plane and parallel the electrostatic deflection was the distance from the upper electrostatic plate to the upper side of the photographic plate. THE FORMULA. Let the two electrostatic plates be separated by a distance d -f- /, d being the air place and t the thickness of the photographic plate, which is of dielectric constant K. The two electrostatic plates are kept at constant potentials V and V". If the plates are separated by an air space of thickness d + t there is a given electric surface density of charge on the plates and, consequently, a given electric force, E, in the space between them. If, now, the dielec- tric of thickness / is introduced, whose equivalent air thickness is t/K, the effective air space will then be reduced from d + / to d + t/K. The effective air space has thereby been reduced an air-equivalent amount of / tjK, causing a change in the capacity. Since the potentials of the two plates have remained constant the surface density and hence the Nous? 1 '] METHOD OF MEASURING e/m AND v. 319 electric force have changed. If, now, the air gap between the two electrostatic plates is increased by an amount t t/K, then the capacity, the surface density and the electric force will resume their former values. If, then, while an electric force, E, exists between the two plates of po- tentials V and F", a dielectric slab of thickness / is introduced and at the same time the plates are further separated by an amount / t/K, making d + 2t t/K in all, the surface density on the plates and hence the electric force, E, will remain constant. The electric force is then given by the equation V - V" = E(d + 2t- t/k), or PD X io 8 E ~ d + 2t - t/k 1 (i) where PD is the potential difference of the two electrostatic plates in volts. The cathode beam in passing through the uniform electric field, E, is accelerated by a constant force and hence follows Newton's second law. The force on the charge e will be Ee = ma, (2) where a is the acceleration toward the positive plate and m is the mass of the electron. Since the electron falls through a distance d in time / we have the distance of fall expressed by the equation d = or 2d =7- (3) If the velocity in the horizontal direction is v and the length of horizontal travel is / we have / = vt, whence i ^ t* I 2 ' Substituting this value in equation (3) gives If this value is placed in equation (2) we have 320 L. T. JONES. [SECOND [SERIES. whence (4) If at the same time the moving electron is subjected to the action of a uniform magnetic field of intensity H and its velocity v is perpendicular to the lines of magnetic force, urging the particle in the path of a circle, in the plane of the photographic plate, then the force is given by mv* Hev = (5) where r is the radius of the circle. If the dotted line, Fig. 3, indicates the path of the particle undeflected by the magnetic field, and the circle of radius r the curvature exper- ienced under the influence of the magnetic field of strength H we may represent the horizontal distance traveled by the length / and the magnetic deflection (measured at right angles to the undeflected path) by 2, since z is small compared with /. Then, from Fig. 3, 2r and Fig. 3. since z 2 , being small in comparison with I 2 , may be neglected. Placing this value of i/r in equation (5) we have e i 22 mv = Hr~ HI 2 ' Elimination of e/m between (4) and (6) gives zE (6) V = Hd' Replacing E by its value given in (i) we get, after simplification, zPD X io 8 ~ Hd(d + 2t- t/K) ' Again, multiplying equations (6) and (7) gives e z 2 PD X 2 X io 8 m ~ H 2 J 2 d(d - t/K) ' (7) (8) THE ELECTROSTATIC FIELD. The two electrostatic plates were rectangular brass plates 7.5X15X1 cm. Considerable difficulty was experienced in getting the two plates No's!"'] METHOD OF MEASURING e/m AND v. 321 sufficiently plane. The plates were first planed and then finished by "spotting" on a master plate. A slip of soft iron 5 X 1.5 X .15 cm. was inlaid in the upper plate, as shown in Fig. 2, and the plate again surfaced. Several days were required to surface the plates but they were finally finished sufficiently plane that one would raise the other from the table. A second slip of soft iron was cut out 5 X 1.5 X .1 cm. and one side made plane. A scratch .005 cm. in width and of about the same depth was drawn full length on this surfaced side. This scratch formed the tube through which the cathode rays passed. The iron slip with the scratch was held against the iron slip inlaid in the upper electrostatic plate by ten brass screws. On account of the small diameter of the scratch and its relatively large length it was subsequently found to be easier to make a scratch of about .05 cm. in diameter, close each end with a small bit of solder, cut off the solder flush with the iron surface and then make a small scratch in the bit of solder at each end. A scratch .1 cm. long at each end was found to give perfect satisfaction, and not nearly so much difficulty was experienced in getting the beam to pass through this tube. In adjusting the cathode to send a beam through the tube the electrostatic plates were first mounted in position with the scratch the full .05 cm. diameter. The vessel was exhausted and a potential difference of about 20 volts applied to the electrostatic plates. The wax joint where the glass tube supporting the cathode entered the plate glass end was then softened by heating and the cathode moved about until a phosphorescent spot on the willemite screen, deposited on the opposite glass end plate, showed the presence of the beam. The wax was allowed to cool while the cathode was in the position giving this spot its maximum brightness. The electrostatic plates were then removed by taking out the screws holding the ebonite disc, B, to the brass ring, D, and the tube made smaller by the bits of solder mentioned above. The plates were then replaced in position and the vessel exhausted. If the spot failed to show on the willemite screen the process was repeated until finally the beam was made to pass through the small tube. An iron tube, /, .5 cm. diameter and 2 cm. long, was screwed into the disc, B, to shield the rays from any magnetic effect before entering the confining tube. The cathode was within I cm. of the tube I. The electrostatic plates were spaced by four hollow ebonite cylinders, one placed at each corner, and clamped in position by ebonite bolts passing through the cylinders. The length of these cylinders was measured by a micrometer caliper reading to .001 cm. The cylinder was placed between two thin glass plates and the length of the whole 322 L. T. JONES. measured. The thickness of the plates was then subtracted. Each cylinder was measured on several successive days and the mean of these measurements was taken as the length. When the cylinders were again measured, after having been in the apparatus under pressure for four months, they were found to have shortened by about I per cent. All data was taken during the first fifteen days, however, so no correction was made for this change in length. The potential difference of the electrostatic plates was determined as follows: A high potential storage battery, 7 s , was used in sending a small current through the two high resistances, M and R, as shown in Fig. 4. M was a resistance of about 2 X io 6 ohms while R was an adjustable resistance of about 10,000 ohms. The electrostatic plates were connected directly to the terminals of M as shown. By adjusting the value of R the potential difference of the terminals of M could be kept constant. The potential drop through a small part of M was meas- ured by a potentiometer, P, against a Weston stand- ard cell of 1.0185 volts at 24 C. The potential dif- ference of the electrostatic Fig. 4. plates was thus easily meas- ured to .1 per cent, and by means of R the value was kept constant to within .1 volt. THE MAGNETIC FIELD. The magnetic field was furnished by a solenoid of 648 turns and 160.2 cm. length. The solenoid was built in two parts and made to join closely at the middle so as to enclose the whole tube. The length of the solenoid was such that the field could be considered uniform and calcu- lated. From the dimensions of the solenoid the strength of the magnetic field at its center was given by H = 5.083 7, where / is the strength of the current in amperes. The current for the magnetic field was supplied by storage cells of 40 amperes capacity. The current, which varied between .5 and 1.5 amperes, was measured by a Siemens & Halske ammeter reading to .005 amperes. RESULTS. In placing the photographic plate in the apparatus for exposure the plate was placed solidly against the ebonite disc, B. The iron confining tube for the cathode beam was 5.08 cm. long and hence a line drawn PHYSICAL REVIEW, VOL. III.. SECOND SERIES. May, 1914. PLATE I. To face page 322. No. 18. No. 3. Fig. 5. L. T. JONES. VOL. III.] No. 5. METHOD OF MEASURING e/m AND v. 323 across the plate 5.08 cm. from the end that touched the ebonite disc established the zero. This line, marked in the photographs, was then directly under the opening of the tube. The length of horizontal travel, /, was measured from this line. In photograph 6 two calculations of e/m were made, where the distance / was 4 and 5 cm. respectively. In each photograph the long streamer, second from the top, is the central one, given by zero magnetic field. The two spots immediately on either side are for the magnetic deflection, direct and reversed. The additional spots seen have no significance relative to the value of e/m. The magnetic deflections were accurately measured along the lines drawn parallel to the line marked 0. The reproductions in Fig. 5 are full size. Twenty photographs were taken in succession. Table I. gives the data relative to all these. TABLE I. Plate No. 7 PD. z. i d. t. d+2t _t V X 10-9. XIO-7. ^ MM 1 .460 524.0 .138 4.0 .835 .165 .292 2.866 2.114 2 .450 564.4 .127 4.0 .820 .180 .210 3.158 2.192 3 .890 498.1 .245 4.0 .825 .175 .204 2.715 1.838 4 .8902 639.7 .220 4.0 .830 .160 .177 3.183 1.935 6 .885 425.0 .251 4.0 .811 .179 .199 2.438 1.701 6a .885 425.0 .3116 5.0 .811 .179 .199 3.027 1.678 7a .850 323.5 .325 5.0 .805 .185 .206 2.506 1.508 7b .850 323.5 .371 5.5 .805 .185 .206 2.861 1.624 Ic .850 323.5 .397 6.0 .805 .185 .206 3.061 .563 Sa .8725 323.0 .314 4.5 .805 .185 ,206 2.355 .647 86 .8725 323.0 .372 5.5 .805 .185 .206 2.790 .547 9 .879 320.3 .335 5.0 .810 .180 .200 2.470 .482 Wa .864 301.0 .389 5.0 .825 .165 1.182 2.734 .937 106 .864 301.0 .423 6.0 .825 .165 1.182 2.973 .591 11 .867 299.0 .377 5.0 .826 .164 1.181 2.622 .807 12a .873 298.0 .405 5.0 .826 .164 .181 2.788 .036 126 .873 298.0 .461 6.0 .826 .164 .181 3.173 .832 13 .872 298.0 .382 5.0 .824 .166 .184 2.632 .815 14a .874 284.2 .4335 5.5 .819 .171 .189 2.947 .837 146 .874 284.2 .499 6.5 .819 .171 .189 3.278 1.735 15 .881 247.2 .467 6.0 .817 .173 .192 2.647 1.533 17 .450 248.6 18 .453 246.6 19 .4515 245.3 20 1.289 296.7 .558 5.3 .850 .140 1.153 2.578 1.563 Average 1.748 The value of the dielectric constant of the glass plate was that given by Landolt and Bornstein for " spiegel glas." If the value of K was taken as either 5 or 7 instead of 6 the resulting value of e/m is changed by only 324 L ' T ' JONES ' about .5 per cent. The probable error of the final result, calculated in the usual way from the data in Table I., is 1.5 per cent. SUMMARY The method devised for the determination of e/m and v for cathode rays from a cold cathode is a modification of the usual electrostatic and magnetic deflection photographic method. It has two distinct ad- vantages. 1. Both the electrostatic and magnetic fields are uniform over the entire path of the deflected cathode beam. 2. The electrostatic deflection is kept constant for all strengths of fields employed and thus the inaccuracy in its measurement is eliminated. The mean of twenty successive photographs gave e/m = 1.75 .=*= .03 X io 7 . I wish to express my appreciation to Dr. C. T. Knipp for his kindly suggestions and to Professor A. P. Carman, Director of the Laboratory, for the facilities offered. LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS, January 20, 1914. Reprinted from School Science and Mathematics, Vol. 14, 1914. Pages 555-562. THE DETERMINATION OF E/M FOR CATHODE RAYS AS A LABORATORY EXPERIMENT FOR AN UNDERGRADUATE COURSE IN ELECTRICAL MEASUREMENTS. BY CHAS. T. KNIPP, University of Illinois, Urbana. The numerical value of the ratio of the charge to the mass of the cathode ray particle or electron is no longer a problem for the research laboratory. It is as truly a constant as is the heat of fusion of ice, or Joule's mechanical equivalent, and its value is nearly as accurately knov.n. However, its experimental deter- mination is generally considered to be fraught with manipulative difficulties of considerable moment, which under the ordinary conditions of laboratory equipment makes it an extremely difficult, if not an impossible, experiment for undergraduates. The recent development of the electron theory with its bearing upon the nature of electricity and the probable constitution of matter is so fundamental and far-reaching that it seems quite proper that one or more of these comparatively new and yet apparently more difficult experiments should be included in an undergraduate course in electrical measurements. Hence the fol- lowing elementary theory for the determination of e/m for cath- ode rays is presented as an instructive and practical experiment. For pedagogical reasons the discussion is given as recently pre- sented to a class in electrical measurements for juniors. The apparatus necessary consists of a Braun tube having a pair of electrostatic field plates inside, a three-inch induction coil, and a high potential battery capable of furnishing potential differences up to 500 volts, also a commutator, a simple water resistance and a voltmeter. The more important characteristic properties of the cathode rays are they travel in straight lines and have a high velocity, the electrons composing the rays each carry a negative elementary charge, they are deflected by either a magnetic or an electrostatic field, they apparently have a mass that is 1/1700 that of the hydrogen atom, they may ionize a gas through which they pass. 550 SCHOOL SCIENCE AND MATHEMATICS and upon striking an object they cause that object to emit Roent- gen rays. The charge on the electron and the mass of the electron are severally quite difficult to determine. However, their ratio, e/m, is comparatively easy of measurement. The velocity of the electron also admits of easy measurement. In the theory that fol- lows, the property of the magnetic and electrostatic deflection of these rays is employed. (a.) ELECTROSTATIC DEFLECTION OF A MOVING ELECTRON/ -o^ -^ B FIGURE 1. In Figure 1 let OX = path of undeflected beam. MN = electrostatic field plates. AB = screen. Y = electric force per cm. between plates. d = length of field plates. / = distance of screen from opening O in diaphragm. y = electrostatic deflection on screen. Let the lower plate be charged positively and the upper one negatively, and suppose that the field ends abruptly at the edge of the plates (the error is quite negligible if the plates are close together). The electron in moving through the uniform electric field is urged toward the positive plate with a force Y^ and its equation of motion is where ^ is its acceleration in the v-direction. From which Accel. = = a. m Applying the laws of falling bodies, the deflection becomes -.l fl /2= i- X* JThomson, Conduction of Electricity through Gases, 2d Ed., p. 117. DETERMINATION OF E/M FOR CATHODE RAYS 55? and the velocity downward is given by Ye d Vmn ^ at =,_._ The path of the electron from the edge of the field plates to the screen AB is a straight line, hence the additional deflection down- ward in traveling this distance is , Ye d ld y'-VmnXt-- -- Therefore the whole distance downward is 1 Ye d 2 , Y> d ld 2 mv- m * 2 ' K-' \ & / m }' V V which may be written, -,- (1) mv* where A is a constant depending upon the geometrical data of the discharge tube. It should be noted that the electrostatic de- flection is inversely proportional to the energy of the moving electron. (b.) MAGNETIC DEFLECTION OF A MOVING ELECTRON. For convenience in discussing make the magnetic field coterminous with the electric field. Let the shaded portions in Figure 1 represent the pole pieces. The magnetic lines are then parallel to electric lines of force. As in the electric case, con- sider that the magnetic field ends abruptly at the edge of the pole faces. It was shown by Rowland and others that a moving charged particle is equivalent to a current of electricity, or i = ev, where e is the charge on the particle and v its velocity. A con- ductor carrying a current in a magnetic field is urged by a force at right angles to both the direction of field and current. The mag- nitude of this force is F = Hi = Hev. In a uniform magnetic field the electron, under the action of a constant force at right angles to its direction of motion, moves in a circular path. By a theorem in mechanics its normal accelera- tion towards the center is 558 SCHOOL SCIENCE AND MATHEMATICS a' - ^ , P where p is the radius of the circle; and the force towards the center is equal to massXaccel. = p Hence the equation of motion for a moving electron in a uniform magnetic field is or 1 _ He p lill' This force urges the electron in the ^-direction, i. e., in a direction perpendicular to the plane of the paper. To evaluate 1/p con- struct a circle of diameter 2p and lay off d, the length of pole face, and s mn , the magnetic deflection, as shown in Figure 2. Draw the additional lines indicated. Then, from the similar right angled triangles, it follows that FIGURE 2. 2p from which d 2 = approximately, since s mn is small in comparison with d. Therefore He mv Following the same line of development as in the electrostatic case, the velocity at m, in the ^-direction is given by DETERMINATION OF E/M FOR CATHODE RAYS 559 - d Hed m The additional magnetic deflection is m ? Hence the total manetic deflection becomes f m 'JL M^ ^,H^ l ~ d 2 mv m v mv which may be written "R ' Y9\ 3 = D - ~ { ~ ) where B, as in the electric case, is a constant depending upon the geometrical data of the discharge tube. The magnetic deflection is inversely proportional to the momentum of the moving electron. It should be remarked that both equations (1) and (2) are true for heavy carriers (atomic or molecular) having either positive or negative charges. For coterminous fields A = B. By applying the two fields simultaneously and at the same time giving them the proper directions the spot on the screen will take up its position at some point P, whose co-ordinates are 3-, z. Obviously, under these conditions, either the velocity v, or the ratio e/m may be calculated by combining the two equations. Eliminating v between (1) and (2) gives AY V 4. _ \32cm. > 4 33 cm. - FIGURE 3. where V is the potential difference in volts between the plates M and N. Again, the constant B becomes, since the magnetic field acts over the entire distance OX and hence d = l, I 2 33 2 and Equations (3) and (4) thus become, for this particular tube, and e \i v 2 i-^iP-f- 104 (^ where H, as suggested above, is the magnetic field due to the earth. Now for H either the total intensity or the horizontal com- ponent may be used. The former gives the larger deflection, how- ever the difficulty of inclining the tube at the proper angle is considerable, especially within a building having an iron frame- work, hence it is more reliable and the experiment easier to per- form when using the horizontal component. The vertical com- ponent, while it displaces the spot on the screen to the north or DETERMINATION OF E/M FOR CATHODE RAYS 561 south (depending on the orientation of the tube), introduces no error since the direction of the electrostatic field is reversed in taking readings for each position of the tube. To enable the tube to be placed in these various positions quickly and accurately it should be mounted on a wooden frame that will admit of rota- tion of the tube about a vertical and also a horizontal axis, as shown in Figure 4. The value of H (the horizontal component) at the point in the laboratory where the experiment was per- formed was previously determined by comparison with the value of H out in the open and about one mile from local magnetic disturbances, and was found to be H = .160 FIGURE 4. Typical sets of data are contained in Tables I and II. The con- ditions that obtained in the two sets were the same with one im- portant exception. In Table II the precaution was taken to shield that portion of the Braun tube between the cathode and the dia- phragm O from the earth's magnetic field by wrapping it with two layers of annealed sheet iron. This shield was connected to earth. The effect of the shielding was quite noticeable in that the spot on the screen was brighter and steadier, thus enabling the deflections 562 SCHOOL SCIENCE AND MATHEMATICS to be more accurately read. The values of v are considerable in excess of those obtained by more refined apparatus, while the values of c/m agree indeed very closely with the generally ac- cepted value which is 1.77X10 7 - In fact the apparatus scarcely warrants such close agreement, yet repeated observations with widely different voltages gave values for c/m in excess but a few per cent of the true value. TABLE I. Readings on Screen A 13. Bulb to West II Bulb to East Direct (Reversed || Direct [Reversed Mean Mag. defl. in cm. Mean Electric defl. in cm. V* in Volts t/xio-o e/mXIO-' Z 48 47 47 Y 24 17 14 Z 48 47 47 Y 33 38 43 Z 51 51 5 1 2 Y 24 17 8 2 Z 51 51 51 Y 34 38 43 .13 .2 .2 y .475 1.05 1.60 190 372 542 6.4 7.5 7.2 1.10 1.74 1.66 Average, 1.50 TABLE II. 42 42.5 42 27 20 14 42 42.5 43 37.5 42 47.5 |46 146.5 |47 27.5 19 13 46 47.5 482 38 42 47.5 .2 .225 .25 .525 1.125 1.70 206 409 625 8.4 8.7 9.8 1.93 1.78 1.84 Average, 1.85 In conclusion it is but fair to mention that the preliminary work of testing out this experiment was ably done by F. E. Faulkner and E. A. Reid, seniors in the University. It was presented later as a regular experiment (on trial) before three sections of juniors in electrical engineeering as an experiment in electrical measure- ments. The accuracy of the results and the favor with which the experiment was received seem to warrant the purchase 'of addi- tional tubes and making it a regular experiment to be performed by under-graduates taking a course in exact electrical measure- ments. 2 Unsteady. [Reprinted from the PHYSICAL REVIEW, N.S., Vol. Ill, No. 6, June, 1914.] AN ATTEMPT AT AN ELECTROMAGNETIC EMISSION THEORY OF LIGHT. BY JAKOB KUNZ. THE principle of relativity gives a consistent explanation of the phenomena of aberration of light, of the experiments of Fizeau and Michelson-Morley, and of the increasing mass of the electron as function of the velocity. The new principle rejects the ether, in which according to the older theory light waves are propagated and in which the electric and the magnetic energies have their seat. We are concerned again with actions at a distance, without a medium, but with actions proceeding with the velocity of light. The mathematical simplicity of the original principle of relativity was mainly due to the fact that it used a fundamental constant, the velocity of light c as an absolute constant, so that the Lorentz trans- formation can be applied to Maxwell's equations, which remain un- changed. Recently A. Einstein 1 generalized the original principle and applying it to the field of gravity came to the conclusion that c must not be con- sidered as a constant but as a function of the coordinates. If the con- clusion of this investigation is confirmed by the experiment, then the original theory of relativity fails and if it is not confirmed, the theory of relativity will be beset with great difficulties. In either case it will only be an approximation to the physical reality. If we consider the material bodies as completely separated but exerting forces on each other, then the action at a distance remains incompre- hensible at all events; but if there is no medium, we should expect in accordance with the Newtonian theory of gravity an action at a distance with infinite velocity, and as a matter of fact we do not know whether gravity proceeds with finite or infinite velocity. If however in the theories of relativity it is assumed that the action proceeds with constant or variable finite velocity, then the phenomena become even more mys- terious. The principle of relativity, even in its simple original form, affects our 1 A. Einstein, "Entwurf einer verallgemeinerten Relativitatstheorie," Zeitschrift fur Mathematik und Physik, Band 62, p. 225, 1914. 465 JAKOB KUNZ. notions of space and time. Time, once absolute, dwindles to a mere shadow. The simultaneity of two events and the equality of two time intervals become relative, the parallelogram of velocities appears only as an approximation, an absolutely solid body is impossible and the mass of a body depends on its velocity. When a physical theory which is mathematically complicated and is only an approximation cuts so deeply in our fundamental notions, and renders the phenomena so incomprehensible, the freedom of advancing other theories, which, though more conservative, attempt to coordinate the various phenomena in question should be granted. In the following a theory will be .developed which agrees with that of relativity in many features, but gives an entirely different aspect of the world. i. FUNDAMENTAL ASSUMPTIONS. 1. One of the theories other than that of relativity is the electro- magnetic emission theory of light. It is a compromise between the emis- sion theory and the wave theory. Each electric charge is supposed to be surrounded by an electromagnetic field residing in the medium, which field itself forms the mass of the charge. Thus instead of having a con- tinuous medium, ether, we have as many media as there are electric charges. Each individual electromagnetic field extends throughout the universe, but is essentially concentrated in the immediate neighborhood of the electron. No assumption is made as to the structure of the elementary medium. 2. Maxwell's equations will be applied to the molecular fields. The expressions for the masses of fields at rest will be extended to fields in motion. 3. The velocity of light is always equal to c for a vacuum. While in a mechanical emission theory the velocity v of the source is added geometrically to the velocity c, we have in the present theory, through a process of compensation, the velocity of light always equal to c, and independent of the velocity of the source. The difference between a mechanical emission theory, the undulatory theory and the electro- magnetic emission theory of light can be illustrated by the following figures. The source of light moves with the velocity v per second from A to B towards the observer. In the mechanical emission theory the light par- ticles emitted in the point A with the velocity c would lie after a second on the sphere with radius c and with the center B. Thus the center of the wave front would always coincide with the source itself. In the undulatory theory, where the light is carried through the continuous VOL. Ill I No. 6. . THEORY OF LIGHT. 466 independent medium, the center of the disturbance would always co- incide with the point A in which it has been emitted. In the electro- magnetic emission theory the center of the disturbance would coincide with the moving source but the wave surface would be an ellipsoid of revolution whose equatorial plane is perpendicular to the direction of Fig. 1. Fig. 2. Fig. 3. motion. In the second and third cases the velocity of light is always equal to c. In the second case the motion of the material luminous source has an influence on the optical phenomena, so we could hope to discover the motion of the source with respect to the ether and if the ether were at rest we could hope to discover the absolute motion of the source. This is impossible by mechanical methods according to New- \ \t Fig. 4. Fig. 5. ton's principle of relativity. In the first and third theory we could not discover the absolute motion of the source. The critical velocity c of light in the vacuum is in Maxwell's theory equal to the ratio of the electrostatic to the electromagnetic unit of electric charge. If we consider c as constant and maintain Maxwell's equations unchanged for an electromagnetic field in motion, we consider that ratio of the two units also as independent of the motion. This means that the ratio of the force which on the one hand unit charge exerts upon another charge in a given distance to the force which on the other hand the same unit charge, when in motion exerts upon a magnet is independent of a uniform motion of the whole system. It is sufficient, but not necessary, for this purpose to assume that an electric charge 467 JAKOB KUNZ. exerts upon another charge the same force, no matter whether both are at rest or in uniform motion ; further, that an electric current exerts the same influence upon a magnet independent of the state of rest or of uni- form motion of the whole system. In this way may be explained the facts that the electrostatic field of the earth, revolving round the sun, produces no magnetic effects, and the magnetic field of the earth no electric effects by electromagnetic induction upon bodies which are rigidly connected with the earth. 4. As there is no independent medium like ether, we are only con- cerned with relative motions between charges, magnets, sources of light and observers. An absolute motion of an electromagnetic system with constant velocity in a straight line can not be defined nor measured with optical and electrical methods. The third and fourth assumptions lead to the Lorentz transformation of Maxwell's equations. There is however another transformation carried out by Maxwell and Hertz who found that the essential form of the equations remains unchanged if they are related to a system of axes at rest with respect to the ether or in motion similar to that of a rigid body; in other words, the absolute translation or rotation of a rigid system of bodies has no influence upon its internal electromagnetic phenomena, provided that all bodies of the system, the atomic fields included, take part in the motion. The electric and magnetic fields seem to be rigidly connected with the material bodies. The laws of geometrical optics are therefore independent of the motion of the earth. The question still arises why according to this theory we can only discover relative motions between charges or magnets and between light sources and observers. In the first examples of course the reason lies in the interaction of the fields, but why should the field around a source of light contract in the equatorial plane if it approaches an observer? The reason may lie in the pressure which the light exerts upon the observer and which the observer exerts on the source. It might finally be possible that all the fields with which we can carry our experiments are imbedded as it were in a universal field of force. 2. THE MASS OF THE ELECTRON. An electron moves slowly in a medium whose permeability and dielec- tric constant are equal to unity. It is accompanied by a material electric field which, for small velocities, is symmetrical round about the spherical electron so that in a distance v from the center the electric force E is equal to E = e/r 2 and the magnetic force is equal to H = ev sin &/r 2 = Ev sin #; the magnetic energy per unit volume is equal to THEORY OF LIGHT. 468 2 sn is the mass per unit volume. sin or for fj, = i E 2 sin 2 tf Wi = - 4 7T ing*' a' 47T /z is the permeability and k the dielectric constant. For the following considerations it will be sufficient to put ju and k equal to I. The mass dm of an infinitesimal ring will be equal to : e 2 dm = 7 sin 2 & 2irr 2 dr sin $ d& and the whole mass will be equal to : 2 62 m = -- = Wo, 3 where a is the radius, e the charge of the electron. This mass extends for an isolated electron throughout the whole space, but half of the mass is concentrated in the immediate neighborhood of the electron, that is in a sphere whose radius a\ = 2a. If the electron moves with finite velocity, then the electric field changes in such a way that the lines of electric force rotate towards the equatorial plane, which is perpendicular to the direction of motion v. At the same time the lines of magnetic force accumulate more and more in that plane as the velocity v increases. If finally the critical velocity c is reached, the whole electromagnetic field will be concentrated in that plane and the mass of the electron will increase indefinitely, so that an electric charge can not move with a velocity greater than that of light. We see also that in this limiting case the electron must cease to emit light in the direction of motion. For a velocity v smaller than c we have : E 6 2 (i -|) sin 2 * dm = - 2irr 2 dr sin & dd, 469 JAKOB KUNZ. whence sin 3 # d$ m = -( The integrations are to be extended over the whole field outside the electron. We do not know the shape of the electron, be it at rest or in motion. But there is a tension in the direction of electrical lines of force, and hence a resultant tension acting on the electron, especially round about the equator and the electron will assume the shape of an ellipsoid of revolution. According to the law which governs the equi- librium between internal and external forces, the mass as function of the velocity will be different. The integration will be carried out for three different conditions as follows : I. The electron preserves the shape of a sphere during the motion. 1 The result of the integration is this: 2. The form of the electron changes according to the law a v 2 b = the integration yields the result m the expression which relativity gives for the transversal mass of the electron. 3. The electron changes according to: the integration gives m Q 8v v 2 U 2 - v 2 4; v i6(c 2 - The first formula gives results which are smaller by I ... 3 per cent. than the experimental values of C. E. Guye and S. Ratnowsky, which are however a little larger than those calculated by means of Abraham's 1 J. Kunz, "Determination theorique de la variation de la masse de 1'electron en fonction de la vitesse," Archives des sciences physiques et naturelles de Geneve, 1913- Na e" 1 *] THEORY OF LIGHT. 47O formula. The third formula gives values too large and increasing too rapidly, while the second formula corresponding to relativity is in best agreement with the facts observed. 3. THE ELECTROMAGNETIC MOMENTUM AND THE PRESSURE OF A BEAM OF LIGHT. It follows from Maxwell's equations that there is a tension in the direction of the lines of force, which per unit area perpendicular to the line is equal to the density of the energy. The pressure perpendicular to the lines of force is just as large. It follows that the pressure of a beam of light per unit area is equal to the electromagnetic energy per unit volume. We can now determine this pressure by means of the electro- magnetic mass and momentum. A beam of light consists in the present theory of oscillating and advancing electromagnetic mass. The electric force is perpendicular to the direction of propagation, sin # = I and if jj, = k = i, then E 2 Wi = . 47T The momentum per unit volume is equal to M the energy per unit volume will be I E 2 c* H* and the pressure per unit area is equal to 27T / X \ H = HaCoey U --) then - _ i ~ 2 and * ' ~ Sir a ' this is the energy of the beam per unit volume. If k and ju are both equal to I, then E p = mic 2 = E, m Wi = -; c z or by differentiation m dm = . 471 JAKOB KUNZ. Hence it follows that a source of radiation, which emits energy, loses a part of its electromagnetic mass. The sun loses yearly about io 14 tons of electromagnetic inertia. On the other hand if a body absorbs energy, its mass must increase proportionally to the energy absorbed, and if an electric charge is set in motion, it will have more magnetic energy than at rest. If this electromagnetic mass were granular and could be broken up into smaller units, such as E = hn, then such a unit would have the mass for yellow light mi = 3iF.io~ 33 , about 100,000 times smaller than the mass of the electron at rest. 4. ON NEWTON'S DYNAMICAL EQUATIONS. Every atom possesses at least one electron. If the velocity of an atom changes, the inertia will change also. Newton's dynamical equa- tions require therefore a correction which for all ordinary velocities of material ponderable bodies is insignificant, but which becomes very large, if the velocity v approaches that of light. The law of conservation of mass does not hold rigorously, but the law of conservation of momen- tum remains exact. The total momentum remains constant in an enclosed system of heavy bodies, electrical charges, magnets, currents and sources of light. If a source emits a beam in a definite direction, it will lose momentum and be driven in the opposite direction. If on the other hand an electric wave strikes a charge, or if a beam is absorbed by a surface, then the material bodies gain as much momentum as disappears from the space. A force is defined in Newton's dynamics by the following equation: dt ' but since dM d(mv) dt dt ' mdv vdm F == -|- ~ dt dt and Fdt = m dv -\- v dm. If the mass moves through space dl during time dt, then the increase of energy is equal to : dl dE = Fdl = F-r.dt = Fvdt = dmv 2 -f mvdv = c*dm, at dm(c 2 v 2 ) = mv dv, (v 2 \ m I ~i ] = -7 v dv. C I C THEORY OF LIGHT. 472 This equation has been integrated by Lewis and Tolman. Putting v/c = x, we get: dm _ d(i x 2 ) m ' 2 I x 2 log m = log (i x*)~* + log WQ, m i hence we find again for the increase of the mass the expression given by relativity. The corrected equation of Newton holds not only for the ordinary inert bodies, but also for the radiations in a cavity. In a cavity bounded by perfect mirrors, we may find for the radiant energy E, the expression E = me 2 , or the energy of radiation possesses inertia. If moreover this electro- magnetic inertia is subject to gravity, then the weight of such a cavity will be equal to : If further the electromagnetic mass is at the same time heavy, then the gravity of the earth will exert on a certain body a force in a given point, which depends on the state of motion or rest of the body. An ordinary potential of gravity, as a function of the coordinates, only exists no more, for it now depends on the velocity of the falling body as well. If the electromagnetic mass is subject to gravity, then a beam of light from a fixed star, passing through the field of attraction of the sun, will be attracted and therefore the position of the star will appear displaced. This very important problem may be solved by this phenomenon or also by observations made with pendulums of radioactive substances which are very rich in electrons. Let us consider two geometrically similar pendulums, the first consisting of a radioactive substance, such as radium, the second of non-radioactive substance. We shall assume the weight Mg of the two pendulums to be the same, but the mass M of the radio- active substance to be m\ +. m, where mi shall be subject to gravity, the electromagnetic mass m independent of gravity. The periods of the two pendulums will be _ 1 2 = 27T M . , Mgs 473 JAKOB KUNZ. The radioactive pendulum would have a longer period than the ordi- nary one. I gr. radium contains about 1/13 mgr. more mass in the active state than after the transformations. In recent years it has been shown by Eotvos that for ordinary bodies the inertia is exactly proportional to the weight up to io~ 7 . But nevertheless we have not yet a direct experimental proof that the electromagnetic mass is subject to gravity. 5. THE EXPERIMENT OF MICHELSON-MORLEY. As there is no independent medium, the motion of the earth has no influence upon geometrical optics and the result will remain the same whether we place the interference apparatus of Michelson-Morley in the direction of the motion of the earth or perpendicular to it. Even if the source of light were not connected with the apparatus, but were in motion, as for instance if the light of canal rays were made use of or the light of a star, in no case would we observe a displacement of the inter- ference fringes through a rotation of the apparatus. Here appears a distinct difference between the electromagnetic and the mechanical emission theories. According to the latter theory we should expect an effect in the experiment of Michelson-Morley, if the light were incident from a star. 6. THE EXPERIMENT OF TRONTON AND NOBLE. The energy of an electric condenser of two plane parallel plates is independent of the direction of the motion of the earth ; this experimental fact follows immediately from our assumptions. In the theory of an independent ether however the condenser would possess more energy if the plates were parallel to the velocity v of the earth, than if they were perpendicular to it. A charged and suspended condenser would produce a couple in the first position tending to bring it into the second position. 7. ABERRATION OF THE LIGHT FROM FIXED STARS. While the light of a fixed star travels from the objective A of the tele- scope to 0', the earth moves with the velocity v from to 0'. The phenomenon of aberration was always evidence in favor of an emission theory or led to the assumption of a stationary ether, through which the earth moves. 00' _ v _ sinfr _ $ is the angle of aberration, v/c the constant of aberration of the light from fixed stars. THEORY OF LIGHT. 474 8. THE EXPERIMENTS OF AIRY AND FIZEAU. As the constant of aberration v/c depends only on v and c, Airy thought that it must change, if c changes. He filled therefore the telescope with water and expected a different angle of aberration, as the velocity of light in water is equal to c/r, if r is the index of refraction of water. Airy found however no change of the constant of aberration and he concluded that the water carries the ether with it, so that the velocity v is diminished by the same measure as c. If the water were carrying the ether with it with its own velocity, then no aberration would be possible, it must there- fore communicate to the ether only a fraction of its own velocity. If the oscillating and advancing mass of a beam of light falls upon a transparent substance containing bound electrons, these charges will be set in motion and emit electromagnetic mass themselves. If moreover the substance struck by light is in motion, the electrons will be deviated from their original direction and oscillate in a new path. The light emitted will be perpendicular to this new direction and the original beam of light appears to be deflected from the original direction. A beam of light strikes a column of water with plane surfaces, which move with constant velocity v perpendicular to the beam of light. Let us consider in a given point of Fig. 4 an electron, which, if the water is at rest, under the action of the electric force OE, is deflected in the direc- tion OD. The magnetic force would have no influence. If however the electron together with the water is set in motion with the velocity v, then the magnetic field of the light will act upon the charge in motion tending to deflect it in the direction OF. The resulting deflection and oscillation will be along OE'] the new beam will travel in a path per- pendicular to this direction, that is from to 0'. OD = eE, <*- OF this means that the angle of aberration < is independent of the specific properties k and r of the medium. Hence Fizeau's experiment follows immediately. The water communicates to the beam a part of its own velocity v, so that the beam travels in the direction of v with a velocity u. It will 475 JAKOB KUNZ. strike a point A on the lower side of the layer of water, and be deflected, so that $ represents again the angle of deviation between the real and the observed beam. Now we have v u sm a = y- , r, c = Vr, sm = r sm a sm a r(v u) ~ , r C This angle however is independent of the specific properties of the flowing substance ; hence for the vacuum : r = i, u = o, sin $ = -, c ; = -( - ), ( - w)r> = v, c/ t/ This is according to Fresnel and Fizeau the fraction of the motion, which the flowing water communicates to the beam of light. If we observe a point at rest through a rotating disc of glass, it will appear to be deflected from its natural position. If we use a Roentgen ray instead of a beam of light then r the index of refraction is equal to I and therefore u = o, that is, we would expect that Fizeau's experiment gives a negative result with Roentgen rays. RECENT LITERATURE. The present attempt at an electromagnetic emission theory is based upon the works of Faraday, Maxwell, H. A. Lorentz and other investi- gators. J. J. Thomson especially has in various investigations treated the electromagnetic field of an elementary charge as something individual, endowed with mass, momentum and energy. He has however, so far as I know, not extended the theory to the critical phenomena here treated. Contributions to the present theory have been made by N. R. Campbell in his book on modern electrical theory, by D. Comstock, PHYSICAL REVIEW, 30, p. 267, 1910; R. C. Tolman, PHYSICAL REVIEW, 31, p. 26, 1910; 35, p. 136, 1912; O. M. Stewart, PHYSICAL REVIEW, 32, p. 418, 1911, and J. Kunz, American Journal of Science, 30, p. 313, 1910. LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS, URBANA, ILLINOIS, March 12, 1914. [Reprinted from the PHYSICAL REVIEW, N.S., Vol. IV, No. i, July, 1914.] SOME BRUSH DISCHARGE PHENOMENA PRODUCED BY CONTINUOUS POTENTIALS. BY STANLEY P. FARWELL. INTRODUCTION. WHEN there exists a large difference of potential between a wire and neighboring conductors such as a similar and parallel wire, or a coaxial cylinder, the discharge phenomenon known as corona is likely to occur. For alternating differences of potential, this phenomenon has been extensively studied by Peek, Whitehead, Russell and others. The alternating corona takes the form of a more or less continuous and uniform bluish glow along the wire. The corona produced by continuous potentials has not received so much attention, presumably on account of the fact that its practical bearing on engineering problems is not so great. Watson 1 and Schaffers 2 have carried out experiments on the corona thus produced. Watson has experimented on wires as small as 0.7 mm. and at pressures as low as 360 mm. Schaffers has worked with cylindrical fields, using wires as fine as 0.006 mm. and various sizes of tube and has determined the critical voltage for visual corona at atmos- pheric pressure. DESCRIPTION OF EXPERIMENTS. The writer has been studying the corona as produced by continuous potentials for wires from 0.037 mm. to 1.285 mm. diameter and tubes 3.50 cm. and 4.45 cm. diameter. The relation between difference of potential and current between wire and tube has been studied for at- mospheric pressure for the different sizes of wire; the critical voltage for visual corona has been obtained for pressures from somewhat above atmospheric down to 2.0 mm. of mercury and the character of the dis- charge noted; and the effect of variation of voltage for a constant low pressure has been investigated. The object of this paper is to present especially some of the phenomena observed at these lower pressures, the influence of a short arc in series with the apparatus upon the character of the discharge, and the increase of pressure in the tube due to the ionization. 1 Watson, Electrician, Sept. 3, 1909, Feb. n, 1910, Feb. 18, 1910. 2 Schaffers, Comptes Rendus, July, 1913, p. 203. 32 STANLEY P. FARWELL. INFLUENCE OF PRESSURE UPON CHARACTER OF DISCHARGE. The series of photographs in Fig. I represents the change in the dis- charge when the wire is negative to the tube and the pressure in the tube is varied from a low value up to atmospheric. The wire was No. 30 B. & S. (0.26 mm. diameter) bare copper taken from a coil obtained from the manufacturer. A glass tube 25 cm. long was lined with a brass sheath, except for a slit 6 mm. wide extending from end to end, and having an internal diameter of 3.5 cm. The wire was stretched tightly along the axis, passing through glass plates at the ends. The tube was rendered air tight by sealing wax and it could be exhausted through a branch tube attached to the side of the cylinder. For the lowest pressures, the discharge takes the form of brilliant beads encircling the wire. Each has a bright cylindrical core, outside of which is a dark space which in turn is surrounded by a purplish glow extending out for some distance from the wire. As the pressure is increased, the difference of potential required to produce a discharge increases, and the number of beads increases. The central nucleus contracts and the bead becomes more and more like a brush until finally there is a line of brushes along the wire. Each brush consists of a bright spot on one side of the wire, with a fan-like purple glow spreading out from it, the plane of the fan being perpendicular to the axis. With the slit tube, the brushes point in different directions but if a similar test be run on a tube without a slit and one looks along the wire, the bright nuclei are seen to lie all in a plane, with alternate brushes on opposite sides of the wire, as a general rule. As the pressure is raised toward atmospheric the isolated brush type of discharge gives place to such a discharge as is pictured in Fig. I for 357.0 mm. pressure. An occasional brush is left, mixed up with a more or less continuous glow which is very irregular. For atmospheric pressure, the discharge looks like the upper picture. The isolated brushes are very few, the rest of the wire presents an extremely "messy" appearance, the glow is bright and purplish and the discharge seems in constant movement. For the lower pressures, a slight increase of voltage above that required to produce beads is sufficient to produce a violet arc-like discharge across the gap between wire and tube at one or two points and if this discharge be allowed to continue, the wire will be burned in two. The photographs for 261.8 mm. pressure in Fig. 2 show the transition from one form of discharge to another, as it takes place for somewhat higher pressures. At the critical voltage, a continuous glow appears. Then as the voltage is raised slightly, the glow becomes spotted, followed, N^'i! V '] BRUSH DISCHARGE PHENOMENA. 33 at a higher voltage, by the gradual breaking up of the glow into the isolated brush form of discharge. Sometimes this process is not so gradual as here indicated. Suppose a difference of potential be im- pressed of a value above that required to just produce a glow. At the instant of closing the circuit, one sees a continuous glow which dissolves into the brush discharge, the brushes emerging one by one, until the entire wire is strung with them. The upper picture illustrates the regu- larity of spacing of the brushes, which will be taken up later. The characteristic appearance of the discharge with the wire positive is that of continuous, uniform, bluish glow of diameter little greater than that of the wire. Its appearance is not noticeably changed by changes in pressure, but it gets brighter with increasing difference of potential. EFFECT UPON DISCHARGE OF AN ARC IN SERIES. The effect upon the discharge of a short arc in series with the apparatus is shown in Fig. 2 for a pressure of 1 12.6 mm. When the wire is positive, the introduction of an arc causes the glow to brighten, increase in diameter, become more purple, and more ill defined as to boundary. The currents recorded on the photographs are obtained from the deflections of a D'Arsonval galvanometer. When the arc is introduced, the current so obtained is much less than one would expect from the small increase in resistance of the circuit caused by the arc. Evidently the discharge with arc in series is made up of two forms of discharge superimposed; the effect due to the continuous potential and an alternating effect caused by the oscillations set up in the circuit by the arc. This superposition of effects is clearly illustrated when the wire is negative. The arc here causes a marked change in the discharge. The result is a continuous glow with a few isolated brushes strewn along it. To test out the effect produced by the arc in apparently producing oscillations in the circuit, a condenser was connected across the cylindrical field. The introduction of the condenser caused the discharge to take the same form it had before the arc was introduced, except for there being a few less brushes. When there is a condenser thus in the circuit and the switch is closed, the transition from a continuous negative glow to the brush form of discharge is prolonged. With the condenser still in the circuit, the disconnection of the impressed difference of potential gives an opportunity for a discharge of the condenser across the cylindrical field. At the instant the line circuit is opened, no change in the appear- ance of the brushes is noticeable. Then as the condenser discharges and its potential falls, there is presented a "moving picture" of the stages of the discharge down to darkness. This discharge was a matter of several 34 STANLEY P. FARWELL. seconds. As the voltage fell, the brush type of discharge was main- tained: each regular arrangement of brushes giving place to another regular arrangement of fewer brushes. Since the resistance of the field is large, the condenser discharge must be of the continuous type. DISCHARGE BETWEEN PARALLEL WIRES. Two No. 34 copper wires were placed parallel and 2 cm. apart inside a tube of glass 25 cm. long and the photographs of Fig. 3 were taken for pressures less than atmospheric. The tendency of the negative wire to show an isolated brush discharge and the positive to give a continuous glow is evident here. There is evidently a tendency for the positive sections of continuous glow to break up into spots or streamers. For constant pressure, the increase of the number of sections of the discharge with increase of voltage will be noted. The spacing of the sections is approximately regular and would undoubtedly be more so if the wires were more exactly parallel and stretched more tightly to make them straighter. The two upper photographs show the effect produced by an arc in series. There is no longer the great difference between the appearance of the two wires. The negative wire, however, still shows a tendency to discontinuity of discharge. When the current is sufficiently great, violet streamers cross between the wires as shown in the upper picture. The current indicated is, again, only the component given by the galvano- meter. SPACING OF BRUSHES AS A FUNCTION OF THE VOLTAGE. The slit tube previously described was fitted with an arrangement for stretching the wire tighter and a series of photographs was taken of the discharge under constant pressure, with the wire negative and varying difference of potential. This series is shown in Fig. 4. The lowest picture shows the appearance of the discharge at a voltage little higher than that required to produce visual corona. It will be noticed that there are many tiny brushes and no regularity of spacing. For a little higher voltage, the number of small brushes has decreased and there are a number of large brushes disposed at quite regular intervals. The succeeding photographs show the effect of increasing the voltage still further. The number of brushes continually increases and the spacing is very regular. For the lower voltages, the brushes are fixed in position for a given voltage and will always show up in the same position as the circuit is interrupted and then closed again. When the voltage ap- proaches the value at which there will be an arc between wire and tube, each brush is in constant movement back and forth in a short path, but the number of brushes is constant for a given voltage. VOL. IV.l No. i. BRUSH DISCHARGE PHENOMENA. 35 Fig. 5 shows the relation between difference of potential and current. In connection with this graph it might be noted that the critical voltage for visual corona was 2,440. It would appear from a close observation of the character and spacing of the brushes that there are only certain voltages for which there appears a regular distribution of full-sized brushes. For intermediate voltages, 16 15 14 12 I" ^10 V 8 k \ / / J / / / 1 / / / ,/* J& **" ^, *>*y j **. f Z L6 ZJ id Z9 5.0 5.1 M 3J J.4 J5 36 37 38 J9 40 41 DIFFERENCE OF POTENTIAL IN KILOVOLTS Fig. 5. there is more or less irregularity in the size of the brushes and their spacing. For the pictures of Fig. 4 an effort was made to pick outjthose points at which the distribution was the most regular. Fig. 6 shows, the vari- IN 10 * * i I '5 ( t g A - x ^ ^ r 1ft P^ X / j^ ** ( x" y- * , " r , r t ^ < CL K'f^ ^-^*^ r- -e- I Fig. 6. ation with the difference of potential of the number of full-sized brushes and the current per brush. When there was a marked variation in the size of the brushes an estimate was made of the equivalent number of full-sized brushes. These graphs clearly indicate that a definite relation exists between the voltage and the number of brushes, for a given pressure, and that the current per brush is not a constant but also varies with the voltage. 36 STANLEY P. FARWELL. The question may be raised as to whether the isolated brush form of discharge may not be due to oscillations in the circuit. In order to make it clear that this is essentially a direct current phenomenon, there is given below a description of the generating apparatus used in producing the continuous potentials and some experiments and arguments which support this view. The source of electromotive force was a battery of small direct-current generators, self -excited and connected in series. The machines were rated at 500 volts and 250 watts and there were thirty in all, giving 15,000 volts at normal voltage. The machines were arranged in two sets, ten in one and twenty in the other, each set being driven by its own direct current motor. Variation of voltage was obtained by field control of the generators and of one of the motors. To prevent damage to the machines through short-circuits, a water resistance of a rather large value was connected between the generating apparatus and the tube. The negative terminal of the machines was grounded. Electrostatic voltmeters were used to measure the difference of potential and a D'Ar- sonval galvanometer in connection with an Ayrton shunt box to give the current. The appearance of the brushes and the current indicated by the gal- vanometer are constant for a given voltage, no matter what combination of machines are used as the source of potential. One of the sets may be used and the appearance of the spots and the voltage and current noted. Then if the other set be used to give the same voltage with a different number and speed of machines, the same results are obtained. If there were oscillations set up perhaps by sparking at the brushes, we would not expect this agreement. Mention has been made before of the effect of the introduction of a condenser in parallel with the tube. To test whether the current sent through the tube by the condenser in discharging was direct or oscillatory, another experiment was performed. The condenser was connected across the positive and negative bus-bars to which the generating ap- paratus was connected through the water resistance. Then a switch connecting the machines to the bus-bars was closed as was also a switch leading to the tube. The deflection of the galvanometer was noted and the appearance of the brushes. Then the generator switch was opened and the condenser discharged through the tube and the galvanometer. After the switch was opened, the galvanometer deflection gradually decreased, the rate of decrease of the deflection being slower and slower as the discharge proceeded. The opening of the switch caused no im- mediate change in the brushes, only the gradual change already noted. BRUSH DISCHARGE PHENOMENA. 37 That the discharge of the condenser must be continuous is shown by the deflection of the galvanometer and it can be further proved by a rough calculation. Assuming the resistance of the cylindrical field as given by E/I and taking a set of values of E and I for the comparatively low pressures at which the brushes are best formed, we obtain R = 1.83 X 10 ohms. Assuming the very large value of o.i henry for the in- ductance of the circuit, and the approximate value of 2 mf. for the capacity, we find the R is about 4.1 X io 4 times as great as ^^L/C and hence it is clear that the condenser discharge must be of the con- tinuous type. By running wires from the terminals of an induction coil to the central wire and the tube and then adjusting the discharge points on the coil to such a distance that a silent discharge took place between them, it was possible to obtain an almost uniform hazy glow along the wire. But no effect could be obtained like -the uniformly spaced brush discharge. It is well known that an arc is the source of electrical oscillations and it has been shown by a previous figure that a short arc in series with the tube disturbs the brushes due to the direct current by the superposition of an alternating current effect so that the glow becomes more or less uniform and the difference in the appearance of the glow for different polarities becomes much less. So the introduction of an oscillatory current acts to suppress the isolated brush form of discharge and not to cause it. The difference between positive and negative electricity is hardly better demonstrated by any other phenomenon. It should be stated here, however, that Peek 1 by a stroboscopic method has also observed "more or less evenly spaced beads" on the negative wire when there was corona between parallel wires caused by an alternating difference of potential of 80,000 volts at atmospheric pressure. The wires used by Peek were 0.168 cm. in diameter, spaced 12.7 cm. apart. EFFECT OF MAGNETIC FIELD. A strong horseshoe electromagnet was placed in various positions with its poles against the tube and the effect upon the various forms of dis- charge of making and breaking the magnet circuit was observed. No change could be noted in the appearance of the discharge or the current flowing. VARIATION OF PRESSURE IN TUBE WITH VOLTAGE. A No. 36 B. & S. copper wire, 0.135 mm. in diameter, was stretched tightly along the axis of a brass tube 4.45 cm. in diameter and closed at 1 Proc. A. I. E. E., Vol. 31, No. 6, p. 1123 and Plate LXV. STANLEY P. FARWELL. [SECOND [SERIES. the ends by glass plates through which the wire passed. A small branch tube was soldered to the side of the main tube and from it connection was made to an air-pump. An open manometer of small bore con- taining a light oil was connected to the side of the branch tube. Every- thing was rendered airtight after disconnecting the manometer and the tube was exhausted. Then dry air was gradually admitted through a tube containing soda-lime and a wash-bottle containing concentrated sulfuric acid, until the pressure was again atmospheric, 744.0 mm. in this case. The manometer was again connected and various differences of potential impressed. As soon as the voltage reached the critical value to cause an appreciable current to flow, a jump in the columns of the manometer was apparent. This jump occurred lower for the wire negative and it was difficult to tell just the voltage at which it began. When the wire is negative, any little dust particle on it will be sufficient to start a discharge at a lower voltage than would be required to cause a general glow along the whole wire. But for the wire positive, the critical point is very marked and the jump occurs, as closely as one can judge, at the same time that a faint bluish glow is seen along the wire. Fig. 7 shows the increase in the I s I" DIFFERENCE OF POTENTIAL IN KILOVOLTS Fig. 7. pressure as the voltage is raised. This graph has exactly the same ap- pearance as the graph plotted between voltage and current, as one might expect from the theory of the conduction of electricity through gases. It will be noted how the curves for the two polarities cross at low voltages and that the increase of pressure for a given voltage is greatest for negative PHYSICAL REVIEW, VOL. IV., SECOND SERIES. July, 1914- PLATE I To face page 38. 10160 Volte - 3.62 * 10 Amp. 737.6 mm, 3500 Volts 7,63 x 10~ Amp, 112.6 mm- 2200 Volte 3.38 x 10^ Amp. -.- 75*7 mm. i 10 il 12 1:5 It 1.1 16 17 18 10 20 21" "23 23 2* 1600 Volts ' 1 ' 2 :s I- Bffliitfiilimiuiilmi ..'" 3.62 * 10 Amp* 58.0 mm. n ii 12 i;j u l' 10 17 IB 19 20 5r"5"2-55 ' 1800 Volte 1.83 x 10"* Amp. ~ 34.3 ran. 12 1.1 U !."> in 17 IB 1 20 21 "22 23 24 600 Volts 6.39 x 10~ Amp. . - 9.9 ram. ** WIPJ2 NEGATIVE: CHANGES WITH VOLTAGE AMD PRESSURE ## Fig. 1. STANLEY P. FARWELL. : J PHYSICAL REVIEW, VOL. IV., SECOND SERIES. July, 1914- PLATE II To face page 38. Negative Brush Discharge- -1450 volts 4.33 x 10 amp. 46.9 mm Negative! Final Form- 4750 volts 1.89 x 10 amp. 2618 mm Negative: Transition Stage-4460 volts-l*24 x 10 amp. 261.8 mm Negative: Transition Stage-4210 volta-0.72 x 10~ 4 amp.--261.8 rani. Negative: With Arc 4110 volts 2.23 x 10 amp. 112.6 mm, Negative: No Arc -3950 volts -4.65 x 10 amp. 112.6 mm Positive: With Arc 4100 volts 2.17 x l6"\mp. 112.6 mm Positive: No Arc .-.-. 4010 volts-^3.79 x lO^arap. 1126 EVOLUTION OF BRUSH FORM OF NEGATIVE DISCHARGE and , EFFECT OF ARC IN SERIES UPOH FORM OF DISCHARGE Fig. 2. STANLEY P. FARWELL. PHYSICAL REVIEW, VOL, IV., SECOND SERIES July, 1914. PLATE III To face page 38. Arc in Series 8000 Volts 1.80 x lO'^Arap. S12.2 mm* Arc in Series 8000 Volts 1.14 x 1(T* Amp. 512.2 No Arc- 8000 Volts 2S x 10"** Amp. 312, 2 nan, Ho Arc 8700 Volts- 450.0 mm. Ho Arc --- - ----- -8400 Volte ----- ; -- -.~~~-~4g0,Q SOME FORMS OP DISCHARGE BETWEEN PARALLEL WIRES Wires-0.165 mm. -2 cm. apart~25 cm. long Upper Wire^is^Negative Fig. 3. STANLEY P. HARWELL. PHYSICAL REVIEW, VOL. IV., SECOND SERIES July, 1914- PLATE IV To face page 38. 3940 Volts ----- 12.2 x 10~ 4 Amp 3870 Volts 10,0 x 10"^ Amp, 3550 Volte 4.65 x 10 3370 Volte - 3*37 x 10~ 4 Amp, 2800 Volts - 1.03 x 10~ 4 Amp, 2700 Volts nnL.L.LLLl., 2500 Volts ---. .33 x lO~ 4 Amp. WIRE NEGATIVEPRESSURE CONSTANT AT 119.3 ma. EFFECT OF VARIATION OF VOLTAGE UPON DISCHARGE Fig. 4. STANLEY P. FARWELL. NoTi! V> ] BRUSH DISCHARGE PHENOMENA. 39 polarity of the wire during the greater part of the range. The crossing of the curves is typical of the voltage-current graphs. In addition to the sudden jump at closure of the circuit there is a gradual increase of pressure due to the heating effect of the current and hence care was taken to read the heights of the columns of liquid as soon as possible after the circuit was closed. The work upon which this paper is based was performed in the labor- atory of physics at the University of Illinois under the direction of Dr. Jacob Kunz, asst. prof, of physics. To him and to Prof. E. B. Paine, of the electrical engineering department, the writer wishes to acknowledge his indebtedness for many helpful suggestions as to the conduct of this work. LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS, April, 1914. [Reprinted from SCIENCE, N. 8., Vol. XL1L, No. 1072, Pages 93-94, July 16, 1915} THE DIFFUSION OF GASES AT LOW PRESSURES MADE VISIBLE BY COLOR EFFECTS AN interesting and instructive experiment for the lecture table is to connect a discharge tube AC, which is about one meter or more in length and which has the exhaust nipple at one end, to a pump that will give a Geissler vacuum an oil Geryk pump will answer very well. Between the pump connection M and the valve that closes the tube there should be fused a side branch N also having a valve. Connect N by a rubber tube to some source of gas other than air, e. g. t ordinary illuminating gas. The connection at M should be made direct to the pump. Connect A and C to the terminals of an induction coil that will give a spark in air five or more centimeters long. To operate, close the valve in the branch N, open and evacuate the discharge tube to the point where on sparking the characteris- tic strisB show distinctly. It is immaterial whether A or C is the cathode, or whether the discharge is unidirectional. Now close the valve 0, and, with the pump still running, open N partly, allowing illuminating gas to be drawn by the pump through the branch OM, thus displacing the air by the gas. By closing N, pumping and later admitting more gas, every trace of air may be washed out of FIG, 1. the tube leading up to 0. Now with N closed allow the pump to run for a few seconds until it is judged that the pressure in the connect- ing tube M is about that in the discharge tube A 0. At this stage everything is in readiness for the experiment, namely, the diffusion of gases at low pressures made visible by the color ef- fect. The well-known characteristic color of the discharge in the case of residual air, con- taining possibly some water vapor, is orange red. To now introduce the illuminating gas open the valve for a moment, then close it. The end of the discharge tube is instantly filled with a beautiful greenish-white color characteristic of illuminating gas. This color will diffuse slowly towards A., each color pal- ing out, and after three or four minutes the discharge throughout the tube will assume a uniform grayish hue. The rate of diffusion is surprisingly slow and of course depends upon a number of factors, e. g., the gas pres- sure in the tube, the pressure of the gas that is admitted, the ionization within the tube due to the discharge passing through the tube, the amount of moisture present, etc. If now the gas connection at N be removed and this stem opened to the air the pump and connections may be freed of gas and the in- verse experiment performed; namely, that of introducing a small quantity of air. The re- sulting orange red color and its diffusion through the grayish hue of the illuminating gas is even more striking than the first. The success of the experiment depends largely upon the skill of the operator in prop- erly proportioning the quantity of gas to be introduced. It is a very simple experiment to perform. OHAS. T. KNIPP LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS, June 2, 1915 (Reprinted from the PHYSICAL REVIEW, N.S., Vol. VI, No. 2, August, 1915] ON THE PRESENT THEORY OF MAGNETISM. BY JAKOB KUNZ. ~^HE electron theory seems to account for the magnetic phenomena in a very direct way. Indeed we have only to assume that the molecular currents of Ampere, which form the elementary magnets, are revolving electrons in order to express Ampere's theory of magnetism in terms of the electron theory. Nevertheless it was only on the basis of the researches of P. Curie that P. Langevin was able to account for the difference in diamagnetism and paramagnetism. Curie found that the diamagnetic susceptibility is independent of the temperature while the paramagnetic susceptibility is inversely proportional to the absolute temperature. Langevin concluded that there is a fundamental difference between diamagnetic and paramagnetic properties. In Langevin's theory the diamagnetism is a characteristic property of each atom which contains a certain number of revolving electrons. If the resultant magnetic moment of these electrons for an external point is zero, then the body is diamagnetic, the action of an external magnetic field consists in a change of the orbit, giving rise to the diamagnetic modification of the atom. If the revolving electrons possess a resultant magnetic moment, the body is paramagnetic. Matter in all its forms is dia- magnetic; paramagnetism, whenever it appears, covers as it were the diamagnetism, and there is no transition between the two distinct groups. We shall add a short deduction of the diamagnetic suscepti- bility. We consider in a diamagnetic gas an atom with an electronic orbit, of radius r, the electron e revolving with velocity v, in a plane perpendicular to the magnetic field. The moment will be equal to M = Trr 2 (e/T) without magnetic field; if a field H is applied, the time of vibration T and the angular velocity will change, so that dM = e-7r\-dr dTj , or neglecting the first part dT 114 JAKOB KUNZ. mv 2 mv 2 = /. f or/ = --, mv 2 mv 2 Hev mv 2 Hev -T = fr' ~ Hev; -^- = / - = ~ r -- wz; 2 Hev [i i 1 He r^ 2 ~" T^J = ~f' "' dT _ dT _ He m ^ T 2 ~ He] T 2 ~ 4irm' dM = H. 4m If there are N orbits per unit volume and if the axes are uniformly dis- tributed in all directions, then we have e 2 r 2 N Tl e 2 r 2 N M = H , or k = . I2m I2m Apparently N and r are independent of the temperature. This theory of Langevin of the diamagnetic susceptibility k is at the same time the theory of the Zeeman effect. In order to find the expression for the paramagnetic susceptibility fo a gas, we shall use a method quite different from that of Langevin. Let the angle between an external magnetic field H and the direction of the moment M of an elementary magnet be equal to a, the work required in order to rotate the magnetic particle from the direction H into its present direction will be equal to W = MH cos a + C; the heat of the gas will change by this amount, and in order to keep the temperature constant, we have to add a quantity of heat Q = W = MH cos a, and the increase of entropy will be equal to S = (Q/T) = (MH cos a/7 1 ) ; and this entropy will be proportional to the lograithm of the probability P that we find the magnet in the direction a MH cos a S = R log P + const. = , M H cos a _ and the number of magnets which are found in an angular interval da will be proportional to P, or MHcosa dn = Ke -dco, VOT VT 1 No 2 J ON TH E PRESENT THEORY OF MAGNETISM. 115 where du = 27r sin a da, MH cos a dn = Ke ^= 2ir sin a da, J\l the total number N of molecules per unit volume will be N = 2irK f e acosa sinada, where we put a for (MH/RT), N = sin ha a and the intensity of magnetization 3? becomes: M cos a dw ' cos ha sin fia The maximum value of the intensity of magnetization $ m = MN, hence m i\ _ /i 2 4 Neglecting the higher powers of a = MH/RT we find 9 = 3 --- x? ^ 3RT - that is, the paramagnetic susceptibility is inversely proportional to the absolute temperature; that is the rule of Curie. EXPERIMENTAL FACTS. The phenomena are far more complicated than the theory of Langevin indicates. The investigations of H. DuBois, K. Honda, M. Owen, Kamerlingh Onnes, P. Weiss, A. Perrier and others have revealed a very large variety of phenomena, in which the rules of Curie are altogether exceptions so that we have to extend or abandon the present theories. The diamagnetic susceptibility should be an atomic property, which is independent of temperature, of a change of state, of a polymorphic transformation or of chemical combination. This is not the case. For instance, the diamagnetic susceptibility of amorphous carbon, of Cu, Zn, Zr, Cd, 3? n > Sb, Te, Tl, 3, Pb, Bi, decreases with increasing tempera- ture, k in the melting of Ag, Sn, Sb, Ga, Ge, Au, Hg, Tl, Pb, Bi changes I 1 6 JAKOB KUNZ. discontinuously. In the polymorphic transformation of C, S, Sn, and Tl the susceptibility changes abruptly, even the sign changes in the poly- morphic transformation and during the melting process of tin. In the case of boron (0-400 C.), diamond, silver and iodine (0-114) the dia- magnetic susceptibility increases with the temperature. There are only a few elements whose diamagnetic k remains constant within a certain interval of temperature; the diamagnetic susceptibility of an inorganic compound is not an additive property. Oxygen, for instance, is a strongly paramagnetic element, but if it combines with the paramagnetic elements of Be, Mg, Al, Mo, W, Th, it forms diamagnetic oxides. And in general the diamagnetic and paramagnetic properties depend so much on physical and chemical influences, that one might be inclined to ascribe them to electrons which are revolving on the surface of the atom. In organic compounds, at all events, it has been shown by P. Pascal that the molecular susceptibility X is an additive property of the atomic susceptibility. Oxygen in these compounds may be para- or dia- magnetic. In more complicated compounds, the structure has a great influence on X. The diamagnetic constants are on the whole not smaller than the positive paramagnetic values. The diamagnetic susceptibility of graphite is greater than the para- magnetic susceptibility of such an element as manganese, one of the strongest paramagnetic elements; charcoal, bismuth and antimony have also large negative susceptibilities. Besides in the crystals of graphite and 'antimony k varies with the direction of the axes. All these facts seem to indicate that what we observe is the difference between a positive and negative magnetism. A similar variety of phenomena is observed in paramagnetism. Oxygen follows Curie's law at ordinary and at higher temperatures, but at lower temperatures the susceptibility varies inversely as the square root of the absolute temperature and finally probably becomes constant. Over certain intervals of temperature the susceptibility remains constant in the elements: Na, Al, K, V, Cr, Nb, W, Os, and even increases with increasing temperature in the case of Ti, V, Cr, Mn, Mo, Ru, Rh, $r, Th. The ferromagnetic metals above the critical temperature, where the ferromagnetism disappears, seem to follow Curie's law, probably with the exceptions of the compounds Fe3O 4 and pyrrhotite. An extension of Langevin's theory is necessary both for the dia- magnetic and the paramagnetic susceptibility. In the first place, in Langevin's theory it is silently assumed that the moments of the ele- mentary magnets are independent of the temperature. This assumption is by no means self-evident. The electrons revolve in the outer layers NOL aT 1 '] ON THE PRESENT THEORY OF MAGNETISM. I I 7 of the atoms probably and the moment of a molecule is the resultant of the moments of the atoms. With increasing temperature we have reasons to believe, the atoms share the energy of temperature agitation and the resultant moment of the molecule may be affected. Besides the fact that the diamagnetic susceptibility changes abruptly, in polymorphic transformations, in changes of state, in chemical transformations, indicates, that the diamagnetism is not simply an additive atomic prop- erty. In general we have to put: M = M f(T). In the second place Langevin's theory of paramagnetism applies only to gases and dilute solutions. The resultant magnetic moment per unit volume depends only on the directing power of the field and on the "scattering" power of the temperature agitation. The equilibrium between these two effects leads to Curie's rule. But as soon as we con- sider a more condensed state of aggregation, the molecules will exert an influence on each other, and this influence for crystals will vary in different directions. P. Weiss has indeed extended Langevin's theory to ferromagnetic substances by adding to the external field H an internal or molecular field N$> which is proportional to the intensity 3 of magnetiza- tion. In this way P. Weiss was able to explain a large number of phe- nomena of ferromagnetic crystals. A similar influence however must exist in paramagnetic solid and liquid substances. The mutual action of the molecules will be a certain function of the temperature f(T) and will in general oppose the tendency of the external field to direct the elementary magnets, just as the temperature agitation; so that the energy of the opposing forces may be written in the form; RT K/T f( 7""^ TT the parameter a will now be equal to p ^ , r /^ N and 3 will become : Kl cos ha or approximately: [M,f(T)fN if f(T) is a constant, for instance, equal to I and f\(T) also a constant QR, then we find Il8 JAKOB KUNZ. [SECOND LoERIES. MfN BR) or k(T + 6) = constant, a result which has been deduced by E. Oosterhuis 1 from Planck's theory of quanta of energy by entirely different considerations. At very low temperatures the specific heat of all substances seems to approach zero, the coefficient of expansion approaches zero also, the electrical conduc- tivity of metals becomes very large, if not infinite, the thermal conduc- tivity increases rapidly. All these properties can be explained by the assumption that at these very low temperatures in the neighborhood of the absolute zero the molecules gradually lose their mobility, and a given substance at absolute zero is a real solid body, as it were one large molecule, where the molecular mobility has disappeared; that means that the influence of the temperature agitation of the individual ele- mentary magnets becomes weaker and weaker and that we can not even define the molecular magnet, because the whole system of magnets is as it were solidified, so that even at the absolute zero saturation of a sub- stance is impossible and that the influence of temperature becomes smaller and smaller or the paramagnetic susceptibility becomes constant. This seems to be the tendency of solid oxygen. If now at the lowest temperatures the function ([f(T)] 2 /RT +/i(r)) is a constant, and at rather high temperatures is equal to i/T and changes continuously from one extreme to the other, then it will in intermediate temperatures be approximately equal to i/T 1 *, and for this interval we shall have: MfN 3 r ' a result which has been obtained by H. Kamerlingh Onnes and A. Perrier for liquid and solid oxygen. The formula k(T + 0) = C or X(T + 9) = C, where X is the molecular susceptibility will be tested by means of measurements made in Leiden 2 on manganese sulfate. In the next place the free electrons will be considered as contributing to the diamagnetic susceptibility. It has been shown by H. E. Dubois and K. Honda that the diamagnetic susceptibility of amorphous carbon, Cu, Zn, Cd, In, $, Sb, Te, Tb, Pb, Bi, Sb decreases with increasing tem- peratures. The strongest diamagnetic metals are Sb and Bi, which show also a very large Hall effect. The magnetic field seems to act on 1 Die Abweichungen vom Curie'schen Gesetz im Zusammenhang mit der Nullpunktsenergie, Phys. Zeitschrift, Vol. XIV., p. 862, 1913. 2 Leiden, Comm. No. 1326. VOL. VI.l No. 2. ON THE PRESENT THEORY OF MAGNETISM. 119 M n S044H 2 M n S0 4 Tabs. X- 106 Abs. Cioio = 1.18 Tabs. ^106 CK> = 26.5 288.7 66.3 1.92 293.9 82.8 2.82 169.6 111.5 1.905 169.6 144.2 2.83 77.4 247 1.93 77.4 274.8 2.85 70.5 270 1.93 64.9 314.5 2.87 64.9 292 1.93 20.1 603 2.82 20.1 914 1.94 17.8 627 2.78 17.8 1,021 1.94 14.4 636 2.60 14.4 1,233 1.92 the free electrons so that they move in spirals or circles and produce diamagnetism. E. Schrodinger 1 found for the contribution k of the diamagnetism, made by the free electrons: i e 2 k = -i-XW, 3 w where N is the number of free electrons per unit volume, and X the mean free path. The effect, calculated in this way, is 100 times too large for silver and copper, which seems to be another argument against the "free" electrons in metals. Nevertheless the action of temperature on diamagnetism and the fact that Sb and Bi have a large Hall effect and a large negative magnetism indicate that the conduction electrons contribute somewhat to the diamagnetism. THE PERIODIC SYSTEM OF THE ELEMENTS AND THEIR MAGNETIC PROPERTIES. The elements may be arranged in series according to the atomic weights in different ways. A certain periodicity between atomic weights and magnetic properties always appears. If the atomic weights are represented by abscissae and the magnetic susceptibilities as ordinates, the curve obtained is of a most irregular character, representing seven distinct maxima, among which that of the iron group is by far predomi- nating. If only the sign of the magnetic properties is taken into account, one gets the best representation perhaps by the method of the helix due to B. K. Emerson, which is given in Fig. i. The strongly magnetic groups appear on a diameter, where we find Fe, Ni, Co, then Pd, Ru, Rh, then Gd, En, Sm, then Pt, 3r, Os. Moving on the spiral from iron to the right, we meet Mn and Cr, elements which are paramagnetic, but whose strongly magnetic properties appear only in some of their alloys and compounds such as the Heusler alloys, manga- 1 Kinetische Theorie des Magnetismus, Sitz. Ber. der K. Akademie der Wissenschaften, Ila, Bd CXXL, p. 1305, 1912. I2O JAKOB KUNZ. [SECOND [SERIES. nese-antimony, manganese- tin, manganese-zinc, Cr 5 O 9 . On the right hand side from the ferromagnetic elements, there are paramagnetic elements, on the left hand side the diamagnetic elements. Opposite to the magnetic metals there are the inert gases, which seem to be weakly diamagnetic. On the right-hand side of the inert gases we find the alkali metals whose weakly paramagnetic properties are not yet sufficiently known. The strongly magnetic metals, cobalt, nickel and iron, belong to the elements with minimum compressibility, with most complex Jf, Fig. 1. spectra, with complex double salts, with great condensation of mass, the heavy metals. Thus it looks as if condensation of electronic orbits were a maximum in these ferromagnetic metals and that the magnetic properties were related directly or indirectly to the mechanical, optical and chemical properties. It is very remarkable that immediately after the strongly magnetic metals there follow the diamagnetic metals: k Cu -0.66 Ag -1.4 Tb Au -2.6 On the next diameter we have : r& Zn -0.96 Cd -1.16 Ho Hg -2.6 When we move outward on a diameter of the spiral, the diamagnetic N L '2 VI '] ON THE PRESENT THEORY OF MAGNETISM. J 2 I susceptibility increases. The same rule is repeated by chlorine, bromine and iodine; sulphur, selenium and tellurium; phosphorus, arsenic, antimony, bismuth. If a represents the atomic weight, a and j(3 two constants, then the atomic susceptibility can be represented for the last three groups by V" - r +-a - Tl and Ge, Sn, Pb. The few values of X known for these elements show that this magnetic constant increases toward the periphery along the diamagnetic diameter of the spiral. If we travel along the spiral from copper towards zinc and from silver toward cadmium, we find the following values for the atomic suscepti- bilities. 122 JAKOB KUNZ. [|ER?ES! Cu 5.29-10-e A g 14.4-10-6 Zn 8.83 Cd 15.2 Ga $n Ge Sn 5.95 As 5.8 Sb 77.5 Se 24.0 Te 38.9 Br 21.9 3 46.5 With the exceptions of As and Sn the atomic susceptibility increases from the south toward the north of the graphic representation. While in the strongly magnetic metals the susceptibility decreases as we move on the diameter outward, the diamagnetic susceptibility increases when we travel in the same direction. Oxygen occupies an exceptional position through its paramagnetic properties. Its regular diamagnetic properties appear only in some of the organic and inorganic compounds. No theory of magnetism is complete, which is unable to account for the exceptionally high magnetic constants of iron, nickel and cobalt and of the other few ferromagnetic substances like the Heusler alloys. All elements can be divided into an electropositive and an electronegative group; all elements are either para- or diamagnetic. Just as we can try to ascribe the forces of affinity to electrical charges in the atom, we might try to reduce affinity to magnetic forces, or magnetons. It is very inter- esting to note that the strongest positive metals of the alkali group are the weakest paramagnetic elements; and that the most negative elements like F, Cl, Br, !$, are rather strongly diamagnetic. While the chemical properties of the most electropositive and electronegative elements may be explained by electrical forces, it seems possible to think that the mag- netic forces due to magnetic doublets play a similar role in the chemical affinity of the elements with strongly magnetic properties. In this way we should get a periodicity of the magnetic properties as functions of the atomic weight as we have a periodic variation of the electropositive and negative properties of the elements. The graphical presentation of the law of periodicity shows the strongly magnetic metals just opposite to the strongly positive and negative metals. This explanation of the periodic variation of the magnetic properties would obtain strong support if it were possible to prove that all magnetons are identical just as all electrons are identical. But there is very little evidence in favor of the identical nature of all magnetons or elementary magnets as we shall see in the last paragraph. In three investigations 1 published in this journal the moments of the elementary magnets and the charge e have been determined for the following substances. 1 The Absolute Values of the Moments of the Elementary Magnets of Iron, Nickel, and Magnetite, PHYSICAL REVIEW, Vol. XXX., p. 359, 1910. Stifler, PHYSICAL REVIEW, Vol. XXXIII. , p. 268, 1911. P. Gumaer, PHYSICAL REVIEW, Vol. XXXV., p. 288, 1912. ON THE PRESENT THEORY OF MAGNETISM. I2 3 WI020 ,-1020 Fe 5.15 1.60 Fe 3 O 4 2 02 0.90 Ni 3.65 1.54 Co 6.21 1.56 Heusler alloy 1 3.55 1.54 Heusler alloy 2 4.23 2.04 1.53- 10- 20 = e (average). This value of e agrees fairly well with the values obtained by independent methods. On account of the necessary extrapolations it is difficult to obtain higher accuracy. While I used the Langevin-Weiss theory for the determination of the elementary moment m, P. Weiss himself measured the intensities of magnetization at very low temperatures, and found noticeable deviations between the theory and the experiment in the temperature-intensity curve and he found at the same time a common divisor among the molecu- lar intensities of the ferromagnetic substances. He called that divisor the magneton-gram, for which he gave the value 1,123.5. In addition the paramagnetic susceptibility of Fe 3 O4 above the critical temperature showed discontinuities as function of the temperature, which consisted of four straight lines, each of which led to a new determination of the magneton. Finally P. Weiss applied the equation C m = X m T = to solutions of paramagnetic substances containing iron and to a con- siderable number of solid salts. It has been shown, however, by Koenigs- berger and Meslin that the molecular coefficient of magnetization of dis- solved substances is a function of the concentration; at least for some solutions, while for others it seems to be constant. This fact makes it necessary to study solutions infinitely dilute or undissolved substances. The number of magnetons found by Weiss in the various sub'stances is shown by the following series, in which the values coincide nearly with whole numbers. 10.41 28.83 21.89 26.99 21.96 28.94 24.04 29.19 28.03 21.23 27.93 25.05 30.09 17.97 25.99 20.04 27.11 12.12 27.91 20.16 27.69 20.16 124 JAKOB KUNZ. If we displace the decimal point by one cypher to the left, we find again approximately whole numbers, which with one exception are almost as exact as the numbers given by P. Weiss. The numbers of magneton per molecule is rather high and it is not very surprising that in dividing for instance, 32,400 of FeClsby 1,123.5 one finds approximately a whole number, 28.83 or 2.883 respectively. The large number of magnetons shown by the last two columns raises the question as to why those substances are so weakly magnetic, while nickel, being ferromagnetic, possesses at low temperatures only 3 magnetons. In addition, the numbers given by P. Weiss are based on the assumption that the magne- tization of the pure salts and of the solutions varies according to Curie's law down to the absolute zero. As far as I know, this assumption has not yet been tested by experiments. Recently however Auguste Piccard 1 measured with great accuracy the susceptibility of oxygen at 20 C. and found for the moment of the atom: 7.8725 . IO 1 ; dividing this number by 1123.4 one gets 7.007, a whole number again. But in this case H. Kamerlingh Onnes and A. Perrier have shown that at low temperatures the susceptibility of oxygen changes according to the law: 2284 _ If this element does not follow the law of Curie, solid salts and solutions will probably also show deviations, and at the same time the evidence in favor of the magneton will decrease. At all events the number of magnetons seems to vary in the atom of a given element like nickel, which contains 3 magnetons at low temperature, 8 at high temperatures, 9 at the limit of the alloys of iron and nickel, 16 in the solutions. In order to determine the magneton P. Weiss, abandoning the theory, has directly measured' the molecular moments of iron, nickel and cobalt; Auguste Piccard, on the contrary, has used the theory in order to find the mag- neton in spite of the measurements of Kamerlingh Onnes and A. Perrier. If we assume that Curie's law holds down to the absolute zero, we find for the elementary moment of oxygen m = 2.58 -io- 20 . The moment of each individual magneton of Weiss on the other hand would be equal to: 1 Archives de Geneve, Tome XXXV., p. 480, 1913. ON THE PRESENT THEORY OF MAGNETISM. 12$ If we determine the molecular moments by means of Langevin's theory, we find values varying from 2.O2-IO" 22 to 5.i5*io~ 20 for substances so different among each other as oxygen, iron, magnetite and Heusler alloys. These values are of the order of magnitude which we should expect from the theory of quanta by Planck. Let us assume that the kinetic energy of a revolving electron %mv 2 is equal to a whole number z times hn, then we find : wcoV 2 huz - = zhn = - , 2 27T hz cor = . irm i The moment of M of the revolving electron will be equal to : e e hz M = lA = irr 2 - = -- T if we put z = i, we find M = i.83-io~ 20 ; for the frequency n we find 1.63 io 15 , assuming r = 1.5 io~ 8 . Why are these magnetons not sources of light? Not much importance must be attached to this approximate .coincidence of i.83-io~ 20 with the moments determined by means of Langevin's theory. We find indeed about the same magnetic moment without the theory of the quanta, by calculating the velocity of the elec- tron by the equation : mv 2 e 2 = ~ 2 ; putting r = i.5-io~ 8 ; we get n = i.4*io 15 ; M = i.54-io~ 20 . And the question arises again, why does such a magneton not emit light? The difficulty might be removed by admitting a large number of electrons revolving in a circle, instead of one electron. The assumption of one single magneton, identically the same in all substances, seems to require much more experimental support, if it exists at all. LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS, URBANA, ILLINOIS, February 22, 1915. [Reprinted from SCIENCE, N. S., Vol. XLIL, A'o. 1082, Pages 429-430, September 24, 1915] THE ABSORPTION OF AIR BY CHARCOAL COOLED TO THE TEMPERATURE OF LIQUID AIR THE remarkable absorption of certain gases by charcoal cooled to the temperature of liquid air, first pointed out by Ramsay and Soddy, may be exhibited conveniently by either of two simple pieces of apparatus. The first (A in the figure) makes use of the electric dis- charge as an index of the degree of absorption ; while the second (B in the figure) indicates the absorption by the barometric column sup- ported in a vertical tube dipping into a bath of mercury. The general form and dimensions of the discharge-tube and its attached charcoal bulb are indicated in A. The volume of the char- coal used should be approximately equal to that of the discharge tube proper. A vent closed by a valve is included. For the experi- ment to be in its best form the cocoanut char- coal should be freshly burned, and to prevent undue absorption of air when not in use the tube should be partially pumped out and the valve closed. The connections are made as shown in the figure, in which 8 is an alterna- tive spark gap of about one centimeter length in parallel with the discharge tube. Any in- duction coil about the laboratory will answer. To operate, open the valve, then close it tightly, thus allowing the pressure within the tube to become atmospheric. On starting the induction coil the spark will pass at S. Now gently submerge the charcoal bulb in liquid air. In about one minute the spark at 8 will begin to weaken and a stringy discharge will appear between the electrodes of the discharge To'mBuction Ct>.l B tube. Soon the spark at S will cease while the tube will be filled with the characteristic Geiss- ler tube glow. In about four minutes the walls of the discharge tube will begin to flouresce, due to the bombardment of cathode rays. The intensity of this fluorescence will rapidly increase and soon the entire tube will be uniformly filled with a beautiful apple- green color. In about one minute more, five minutes from the start, the greenish color will begin to fade and sparking will reappear at 8 f showing that the vacuum in the tube is be- coming "hard." In short the pressure may thus be reduced from atmospheric to about .001 mm. mercury in five or six minutes with no other agency than that of the absorption of air by charcoal cooled to the temperature of liquid air. The second method of showing the absorp- tion of air, due to Dr. L. T. Jones, is at once clear by an inspection of B in the figure. The vertical stem, up to the branch leading to the charcoal bulb, should be at least 78 cm. long. This stem may also have an enlarge- ment about half way up as shown. A valve should be included to protect the charcoal when not in use. Before starting the exper- iment the valve is opened and the tube mounted in a bath of mercury. Liquid air is then applied to the charcoal bulb. The ab- sorption proceeds slowly at first, but soon gains headway as the charcoal cools. The speed that the mercury column acquires as it rises up through and fills the enlargement is surprising. Even with the ratio of volume of tube to char- coal as shown in the figure (approximately 4 :1) the mercury column will mount to nearly full atmospheric pressure in the short space of five or six minutes. Added interest is to perform the two ex- periments simultaneously. CHAS. T. KNIPP LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS, August, 1915 Acoustics of Auditoriums. INVESTIGATION OF THE ACOUSTICAL PROPERTIES OF THE ARMORY AT THE UNIVERSITY OF ILLINOIS. By F. R. WATSON, Associate Professor of Physics, University of Illinois. (Reprinted from The Brickbvilder, October, 1915.) THE Armory at the University of Illinois presents an unusual case of defective acoustics because of its very large volume and comparatively small absorbing power. It was built to fulfil the usual requirements of an armory in regard to military drills ; but, in addition, it has been used on several occasions for convocations and assemblies where the audiences have been very large. The acoustics proved to be impossible for speaking and music. In view of the proposed continued use of the building for such assemblies, the writer carried on an investigation to determine the possibilities of making it satisfactory in its acoustical properties. The Armory is 400 feet long, 212 feet wide, and 93 feet to the highest point of the roof. Acoustically, it is defective because of echoes and reverberation. Echoes are Fig. 1. Framework of Parabolic Reflector set up by the distant walls, while the reverberation is caused by the undue prolonga- tion of sound. Several experiments were tried to determine the value of special devices for reinforc- ing and directing the sound. In one case, a huge parabolic reflector of special con- struction was used. This was based upon the known action of parabolic reflectors in directing sound along the axis of the parabola.* A modified paraboloid was constructed, the parabolic ribs of which were arranged so as to spread the reflected sound over the entire area occupied by the audience. The framework, pictured in Fig. 1, was covered with oilcloth and mounted over the head of the speaker so that his mouth was at the common focus of all the parabolic ribs. Preliminary tests with the reflector showed that it admirably fulfilled its purpose in *" The Use of Sounding Boards in an Auditorium," Physical Review, Vol. 1(2), p. 241, 1913, and THE BRICKBVILDER, June, 1913, and August, 1913. Fig. 3. Interior of Armory Fig. 4. Interior Arranged for Commencement Exercises directing sound ; but when used at an assembly with an audience, its action was tically drowned out by the excessive reverberation which prohibited any possibil satisfactory acoustics. Another experiment of like nature involved the use of a special megaphone to di ute the sound of the speaker's voice. This megaphone was more efficient ihi reflector, since it utilized all the sound sent out by the speaker instead of on* portion intercepted by the reflector. This device was also of little benefit beca the excessive reverberation. A third trial was made by using a number of loud-speaking telephones at dif positions in the Armory. This attempt was also unsuccessful, although the telep when used out in the open air were very effective in reinforcing and directing the s These experiments showed the impossibility of using the entire Armory for spe purposes unless the reverberation could be materially reduced. The investigatic then directed to the determination of the constants of reverberation and the poss of correcting them. Sabine's method* was used for this- purpose. His forrm reverberation is expressed as follows : where t is the time of reverberation, v the volume of the room, a the sound-absc power of all the exposed surfaces in the room, and k a constant which is deter experimentally. Applying this formula to the case of the Armory, the volume of is 6,652,000 cubic feet, and the total absorbing power, without an audience, units, the time of reverberation was calculated to be 24 seconds. This value is v ally large. The Auditorium at the University of Illinois, seating 2,200 people, reverberation before its acoustical correction of 9 seconds and was considered very bad.f The conditions in the Armory by comparison with this case may be in to be exceptionally unsatisfactory. Calculations made to ascertain the effect of introducing sound-absorbing m; showed that the installation of 50,000 square feet of hairfelt would reduce the reve tion to 4.66 seconds, a value which would still be too large for satisfactory spej The only alternative was to reduce the volume. Calculations were then made f acoustical properties of a room partitioned off by canvas curtains at one end Armory so as to enclose a space 212 feet by 134 feet and 35 feet high. To do 1 was first necessary to determine experimentally the action of the canvas in transn and absorbing sound. The time of reverberation for the room with an audie 4,500 people present was then estimated to be 1.1 seconds, a value which ha; found by repeated experience to be satisfactory. On the basis of this calculation a room of the specified dimensions was enclo one end of the Armory and used for the University Commencement exercises. Fig. 4.) Auditors in all parts of this canvas-enclosed room could hear and unde: the various speakers, so that the room was considered a success from the standp< acoustics. A further step to be undertaken in the investigation lies in the proposed instal of some sound-absorbing materials upon the walls of the Armory itself. It is that by this means the time of reverberation may be reduced to a reasonable leng make the building entirely satisfactory for military drills and band concerts. Wl or not it will also be suitable for assemblies where there is speaking, remains to be [Reprinted from the PHYSICAL REIVEW, N.S., Vol. VI. No. 5, November, 1915.] SATURATION VALUE OF THE INTENSITY OF MAGNETIZA- TION AND THE THEORY OF THE HYSTERESIS LOOP. BY E. H. WILLIAMS. T3 ECENTLY, Weiss 1 has shown that an alloy composed of iron and V\ cobalt combined in relative amounts given by the expression Fe 2 Co gives a much higher value of the intensity of magnetization than either iron or cobalt taken alone. Furthermore, it has been shown by Mr. D. T. Yensen 2 that the magnetic properties of pure iron can be greatly improved by melting the iron in a vacuum and it was hoped that the magnetic properties of Fe2Co could be improved by treating it in like manner. The object of the present paper was not only to make a careful study of the saturation value of the intensity of magnetization of Fe2Co prepared under various conditions but to use the data thus obtained in a test of the theory of the hysteresis loop as developed by J. Kunz. 3 In his paper, Kunz tests the theory with the data then available. The results show the discrepancy between theory and experiment to be very great. If all quantities involved are obtained from the same sample, the test of the theory will be more satisfactory. PREPARATION OF SAMPLES. Iron and cobalt were taken in the proportion indicated by the formula Fe 2 Co, melted in a vacuum furnace under pressures varying from 5 mm. to 0.5 mm. Hg, allowed to cool slowly and then forged into long bars from which samples were turned. In most cases enough of the material was taken to make both an ellipsoid and a rod the ellipsoid for the determination of the saturation value of the intensity of magnetization and the rod for the determination of the hysteresis loop. The hysteresis data were taken by Mr. D. T. Yensen on a magnetic testing apparatus similar to those used by the Bureau of Standards. Mr. Yensen has made a study of the samples from the viewpoint of the engineer. His results are to be published soon in the General Electric Review. 1 P. Weiss, Compt. Rend., 156, p. 1970, 1913. ! D. T. Yensen, Bui. No. 72, Eng. Exp. Sta., Univ. of Illinois, Urbana, 111. ; J. Kunz, Phys. Zeit., XIII. , p. 591, 1912. directing sound ; but when used at an assembly with an audience, its action was prac- tically drowned out by the excessive reverberation which prohibited any possibility of satisfactory acoustics. Another experiment of like nature involved the use of a special megaphone to distrib- ute the sound of the speaker's voice. This megaphone was more efficient than the reflector, since it utilized all the sound sent out by the speaker instead of only the portion intercepted by the reflector. This device was also of little benefit because of the excessive reverberation. A third trial was made by using a number of loud-speaking telephones at different positions in the Armory. This attempt was also unsuccessful, although the telephones when used out in the open air were very effective in reinforcing and directing the sound. These experiments showed the impossibility of using the entire Armory for speaking purposes unless the reverberation could be materially reduced. The investigation was then directed to the determination of the constants of reverberation and the possibility of correcting them. Sabine's method* was used for this- purpose. His formula for reverberation is expressed as follows : where t is the time of reverberation, v the volume of the room, a the sound-absorbing power of all the exposed surfaces in the room, and k a constant which is determined experimentally. Applying this formula to the case of the Armory, the volume of which is 6,652,000 cubic feet, and the total absorbing power, without an audience, 13,400 units, the time of reverberation was calculated to be 24 seconds. This value is unusu- ally large. The Auditorium at the University of Illinois, seating 2,200 people, had a reverberation before its acoustical correction of 9 seconds and was considered to be very bad.f The conditions in the Armory by comparison with this case may be inferred to be exceptionally unsatisfactory. Calculations made to ascertain the effect of introducing sound-absorbing material showed that the installation of 50,000 square feet of hairfelt would reduce the reverbera- tion to 4.66 seconds, a value which would still be too large for satisfactory speaking. The only alternative was to reduce the volume. Calculations were then made for the acoustical properties of a room partitioned off by canvas curtains at one end of the Armory so as to enclose a space 212 feet by 134 feet and 35 feet high. To do this it was first necessary to determine experimentally the action of the canvas in transmitting and absorbing sound. The time of reverberation for the room with an audience of 4,500 people present was then estimated to be 1.1 seconds, a value which has been found by repeated experience to be satisfactory. On the basis of this calculation a room of the specified dimensions was enclosed at one end of the Armory and used for the University Commencement exercises. (See Fig. 4.) Auditors in all parts of this canvas-enclosed room could hear and understand the various speakers, so that the room was considered a success from the standpoint of acoustics. A further step to be undertaken in the investigation lies in the proposed installation of some sound-absorbing materials upon the walls of the Armory itself. It is hoped that by this means the time of reverberation may be reduced to a reasonable length and make the building entirely satisfactory for military drills and band concerts. Whether or not it will also be suitable for assemblies where there is speaking, remains to be seen. * American Architect, 1900. t" Acoustics of Auditoriums," Bulletin No. 73 of the University of Illinois, Engineering Experiment Station. [Reprinted from the PHYSICAL REIVEW, N.S., Vol. VI. No. 5, November, 1915.] SATURATION VALUE OF THE INTENSITY OF MAGNETIZA- TION AND THE THEORY OF THE HYSTERESIS LOOP. BY E. H. WILLIAMS. ECENTLY, Weiss 1 has shown that an alloy composed of iron and cobalt combined in relative amounts given by the expression Fe 2 Co gives a much higher value of the intensity of magnetization than either iron or cobalt taken alone. Furthermore, it has been shown by Mr. D. T. Yensen 2 that the magnetic properties of pure iron can be greatly improved by melting the iron in a vacuum and it was hoped that the magnetic properties of Fe 2 Co could be improved by treating it in like manner. The object of the present paper was not only to make a careful study of the saturation value of the intensity of magnetization of Fe2Co prepared under various conditions but to use the data thus obtained in a test of the theory of the hysteresis loop as developed by J. Kunz. 3 In his paper, Kunz tests the theory with the data then available. The results show the discrepancy between theory and experiment to be very great. If all quantities involved are obtained from the same sample, the test of the theory will be more satisfactory. PREPARATION OF SAMPLES. Iron and cobalt were taken in the proportion indicated by the formula Fe2Co, melted in a vacuum furnace under pressures varying from 5 mm. to 0.5 mm. Hg, allowed to cool slowly and then forged into long bars from which samples were turned. In most cases enough of the material was taken to make both an ellipsoid and a rod the ellipsoid for the determination of the saturation value of the intensity of magnetization and the rod for the determination of the hysteresis loop. The hysteresis data were taken by Mr. D. T. Yensen on a magnetic testing apparatus similar to those used by the Bureau of Standards. Mr. Yensen has made a study of the samples from the viewpoint of the engineer. His results are to be published soon in the General Electric Review. 1 P. Weiss, Compt. Rend., 156, p. 1970, 1913. 5 D. T. Yensen, Bui. No. 72, Eng. Exp. Sta., Univ. of Illinois, Urbana, 111. 5 J. Kunz, Phys. Zeit., XIII. , p. 591, 1912. 4 05 E. H. WILLIAMS. ELLIPSOIDS. A great deal of trouble was experienced in making ellipsoids that were accurate. The form of the ellipsoids was tested by projecting an image of the ellipsoid on the figure of an ellipsoid drawn to the desired pro- portions. Finally the accuracy was tested by comparing the volumes obtained by calculation, using the dimensions of the ellipsoid, with those obtained by immersion in distilled water at known temperature. No ellipsoid was used where the difference in volume differed by more than 2 per cent, and most of them differed by less than I per cent. The ellip- soids were about 1.19 cm. in length and about .56 cm. in diameter. The author wishes to express his thanks to P. Weiss for samples of his material which he kindly sent. This material, when received, was porous and had apparently been melted and cast at atmospheric pressure. One ellipsoid was turned from the material just as received. A second ellipsoid was turned from a portion of the material which had been forged into a small rod, after which the remainder of the sample was remelted in a vacuum furnace under a pressure of .5 mm. of Hg. It was then forged into a rod from which an ellipsoid was turned. The results obtained with these ellipsoids are included in Table I. The field inside an ellipsoid is uniform and is given by H = Ho - NI t (i) where H is the external field applied, / the intensity of magnetization, H the resultant field within the ellipsoid and N a constant depending on the dimensions of the ellipsoid. The field H Q was produced by a large electromagnet the pole pieces of which were 3.2 cm. apart and bored to receive a glass tube 9 mm. in diameter. On this tube was wound an induction helix. The field, H , between the poles of the magnet was calibrated by two methods by means of a flip coil and with a magnetic balance. The mean of the two calibrations, which differed in no case by more than one half of one per cent., was taken to plot the calibration curve. The intensity of magnetization / was obtained by suddenly removing the ellipsoid from the induction helix between the pole pieces and noting the change of flux as indicated by a ballistic galvanometer. From the constants of the apparatus the value of I could be calculated. If, in equation (i), NI is greater than H , H becomes negative while HQ and I are still positive, i. e., the field within the ellipsoid is opposite in direction to the field outside. The ellipsoids used in this work were such as to produce this result, so that when a hysteresis loop was taken with one of the ellipsoids a very peculiar S-shaped form was obtained. INTENSITY OF MAGNETIZATION. 406 RESULTS FOR I m . The results for the saturation values of the intensity of magnetization are summarized in Table I. In this table also, values obtained by other experimenters as well as by the author are given for comparison. An- nealing these samples at 900 C. and 1100 C. produced practically no change in the values of I m . Analysis of the first two samples of Fe 2 Co listed in Table I., were made, the first showing 33.36 per cent. Co and the second 33.33 per cent. Co. From these results we see that com- TABLE I. Values of I m (t = 20 C.) Commercial steel (Williams) 1,751 Swedish wrought iron (Ewing) .1,690 Bessemer steel (.4 per cent. C.) 1,770 Electrolytic iron (melted under pressure of 3 mm. of Hg (Williams) 1,798 Cobalt (1.66 per cent. Fe) (Ewing) 1,310 Cobalt (pure) (Stifler) 1,421 Cobalt (melted under pressure of 1 mm. Hg (about 99 per cent, pure) (Williams) 1,504 Fe2Co melted under pressure of 3 mm. of Hg without being forged (Williams) 1,791 Same hand forged (Williams) 1,962 Same forged with steam hammer (Williams) 1,977 Fe 2 Co melted under pressure of 1 mm. of Hg. Forged with steam hammer (Williams) 2,050 Fe2Co melted under pressure of 0.5 mm. of Hg. Forged with steam hammer (Williams) 2,056 Fe2Co melted and cast at atmospheric pressure (sample re- ceived from P. Weiss) (Williams) 1,752 Same forged as received (Williams) 1,977 Same remelted under .5 mm. pressure and forged (Williams). .2,038 bining pure iron for which the value of I m is 1,800, when the iron is melted in a vacuum, with cobalt for which the value of I m is 1,500 when melted under the same conditions, we obtain an alloy for which I m is 2,050, or 14 per cent, higher than pure iron itself. Weiss, in the paper referred to above, states that if one takes into account the difference in atomic weight, the temperature at which ferromagnetism disappears and the densities, one finds that at ordinary temperatures ferro-cobalt has a magnetization at saturation 10 per cent, higher than that of iron, so that the extra 4 per cent, is probably due to the fact that the alloy in the present case was melted in a vacuum. This conclusion is sub- 407 E. H. WILLIAMS. [SECOND [SERIES. stantiated by the difference between the last two results of Table I. (material received from P. Weiss). This difference is undoubtedly due to melting under greatly reduced pressure since all other conditions are as nearly equal as it was possible to make them. Photomicrographs of the first two samples of Fe 2 Co given in Table I. are shown in Figs. I, 2, 3 and 4. Fig. I is of the first sample after being forged and Fig. 2 is of the same sample after being annealed at 900 C. and cooled uniformly at the rate of 30 C. per hour. Fig. 3 is of the second sample of Fe2Co listed in Table I. after the same had been forged and Fig. 4 is the same sample after being annealed at 900 C. HYSTERESIS THEORY. In the article by J. Kunz referred to above, the author obtains the following expression for the energy of the hysteresis loop: W = 'i + A/! I I rr 2 / (Hi - Atf) 2 I* + /I + A/! where I m is the saturation value of the intensity of magnetization, H e the coercive force, /i the intensity of magnetization corresponding to the magnetizing field HI, and where and According to this theory the hysteresis loss per cycle experienced when the field alternates between the values + HI and HI, producing the intensities of magnetization + I\ and /i, can be calculated directly if one knows the values of I m and H c for the material concerned. As pointed out above, the test given this theory proved very unsatis- factory and seemed to indicate that the theory was of very little practical importance. It seemed desirable to give the theory a thorough test by the careful determination of the four quantities I m , H c , HI and I\ with the same sample. The results for the hysteresis loss, W, calculated and the hysteresis loss, W, as measured from the hysteresis loops are given in PHYSICAL REVIEW, VOL. VI., SECOND SERIES. November, 1915. PLATE I. To face page 408. Fig. 1. FezCo melted under 3 mm. pressure and forged. Fig. 2. Same as Fig. i, annealed at 900 C. Fig. 3. Fe2Co melted under i mm. pressure and forged. Fig. 4. Same as Fig. 3, annealed at 900 C. E. H. WILLIAMS. VOL. VI.l No. 5. J INTENSITY OF MAGNETIZATION. 408 Tables II., III. and IV. Table II. is for a sample of Fe 2 Co before being annealed; Table III. for the same sample after being annealed at 900 C., ust eres/s Curves for Fe^Co after Anneahna at the three roots are 2.42, 1.497 and 0.9210, hence the angle # = 22 55', But as the shell has not everywhere the same thickness, this angle does not accurately indicate the direction in which most of the energy is radiated away. The energy of the electric force E t within the elementary volume 2irp sin dpddd is equal to dE es = --E?2irp sin dpd$8 oTT I v 3 sin 3 4 l(2c v cos &)(c v cos #) 2 ' The electrostatic energy in the cap under the angle $ is given by the integral 4 / ,/ (2C - z; cos $)(c V COS t?) 2 _I' 2 | 3c 2 i> 2 1 c v cos # 4c 2 z; 2 , 2c v cos i? ~4ii C 2 10 S c v c 2 log 2c z; + - -z; 2 r I I -.].} c Lc v cos # c The function sin 3 I? (2C v cos #)(c : V COS #) 2 or sin 3 t? ^ "( ^008 *)( V \ 2 I COS ^ 1 c 1 has been plotted in Fig. 4 for the values v/c = 9/10 and v/c = 99/100. This figure shows clearly that with increasing velocity the energy is radiated away in a direction which approaches more and more the direction of motion of the electron. The bearing of this conclusion on the fluctuations of Schweidler and perhaps on the difference in the JAKOB KUNZ. SECOND SERIES. photoelectric effect according to the incidence of the beam of light, or Roentgen rays is obvious. If we attribute to the electromagnetic field not only energy, but also momentum and mass, then it follows, that the electromagnetic mass of the electron, when it comes to rest, is thrown Fig. 4. forward more and more with increasing velocity. This electromagnetic mass and momentum concentrated in a comparatively small space, is not so very different from the notion of light particles in the old emission theory. UNIVERSITY OF ILLINOIS, LABORATORY OF PHYSICS, May 22, 1915. [Reprinted from the PHYSICAL REVIEW, N. S., Vol. VII, No. i, January, 1916.] ON THE CONSTRUCTION OF SENSITIVE PHOTOELECTRIC CELLS. BY JAKOB KUNZ AND JOEL STEBBINS. THE high sensitiveness of photoelectric cells of alkalihydrides has been discovered by Elster and Geitel. For several years we have tried to apply this cell in stellar photometry. J. G. Kemp 1 and W. F. Schulz 2 have shown that it is possible and advantageous to replace the selenium in stellar photometry by the photoelectric cell. Practically at the same time corresponding measurements have been made in Germany, especially in the observatory of Berlin. One of us has reported on an astronomical discovery made by the photoelectric cell in the Evanston meeting of the American Astronomical Society in September, 1914. In the last two years we have tried to improve the photometric properties of the cell and we have arrived at a form which seems to be satisfactory with respect to sensitiveness, con- stancy, absence of the dark current, etc. The final form is indicated by Fig. i, which is drawn full size. The glass bulb is 3.4 cm. in diameter. It contains a small platinum cathode C, a platinum ring of 1.8 cm. in diameter as an anode A, which passes through a platinum cylinder B] this cylinder was found to be very necessary in order to lead surface and electrolytic currents of the glass to earth. Strips of tinfoil were occa- sionally wrapped around the glass cylinder at D and the cathode C, in order that dark currents might be suppressed. The tubes are connected to the mercury pump and heated two to three hours to 330 C. to drive off the remaining gases. A small quantity of the pure alkali metal is distilled on the silver mirror of the cell, which is kept cool by cold water or ice, at the same time the end AD of the cell is heated from 160 to 240, according to the alkali metal, by means of a heating coil. 1 J. G. Kemp, PHYS. REV., Vol. I., p. 274, 1913. W. F. Schulz, Astrophysical Journal, Vol. XXXVIII, p. 187. 63 JAKOB KUNZ AND JOEL STEBBINS. [IS?Es! The most sensitive cells have been obtained when the metal was deposited in a thin uniform layer. Pure hydrogen from palladium was then admitted and its pressure so adjusted that a potential difference of 280 to 400 volts between the electrodes produced a uniform glow discharge. Often a spark or arc appears instead of the bright uniform glow, and the spark is apt to destroy the sensitive layer. By experience one finds the best conditions for the glow to appear. The sensitiveness will be tested during the formation of the hydride. As a rule the forma- tion requires only one to three seconds for the maximum sensitiveness; if continued, the colors of the compound change and the deflection in the galvanometer decreases. During the formation the electrode C is negative and A positive. But in certain gases like ammonia and ethane a sensitive layer is also formed if the current is reversed. After the formation the gas is carefully pumped out and replaced by an inert gas, helium, argon, or neon. The pressure is so chosen as to get a maximum sensitiveness. Experiments have been made with the object of finding out the influence of the size and shape of the cell on the sensitiveness. The diameter varied from 5 to 2.5 cm. and the sensitiveness rather increased with decreasing diameter. The silver mirror was sometimes deposited on a flat or conical bottom, so that the incident light should be reflected and its action increased; but very little increase in the deflection of the galvanometer was observed, so that the ordinary spherical shape was chosen. Efforts have been made to replace the hydrogen by other gases, for instance ethane, ammonia and acetylene. With ethane and the current reversed a very dark violet-blue color was obtained of a high sensitive- ness, and of a beautiful metallic luster, but unfortunately the sensitive- ness proved not to be constant. When dry ammonia vapor was used instead of hydrogen for the formation, a bright blue layer was obtained of high sensitiveness which however decayed also in the course of time. Acetylene finally formed a black layer with potassium under the influence of the electric field, but it was very little sensitive. So far hydrogen seems to give the most sensitive and the most constant cells. Four alkali metals have been used, viz., sodium, potassium, rubidium and caesium. The best results have been obtained with rubidium and neon. The metal was distilled in the cell while the silver mirror was cooled with ice. A potential difference of 280 volts produced a glow in the hydrogen and a very beautiful violet reddish sensitive layer with a bright metallic luster. The hydrogen was then replaced by helium, argon or neon. The neon was received from the Bureau of Standards. VOL. VII.1 No. i. SENSITIVE PHOTOELECTRIC CELLS. 6 4 The three curves A, B and C, of Fig. 2 show the relative sensitiveness of the rubidium cells filled with these three gases. Helium gives the smallest, neon the best sensitiveness. Nevertheless it is possible that the helium and argon cells are better than the neon cell because the curve for the neon rises much quicker than the other curves, in other words the neon cell is more sensitive to small changes of the potential difference acting between the electrodes than the helium and argon cell. It is very important to use perfectly pure gases. The sensitiveness of some cells decays slightly during the first few days after the formation and then becomes constant. Some distinct white spots appeared on the surface of some of the very bright violet rubidium metals, and in one or two instances such a spot became wider Fig. 2. in the course of time and covered finally the whole surface, which then appeared bright bluish, and whose sensitiveness was considerably less than that of the original violet surface. When the cells were of a larger size, these bright violet-red surfaces on rubidium were never obtained, but rather sky-blue and blue-green colors which exhibit very beautiful iridescence. The potassium cells were formed with a potential difference of 360 volts. The glow discharge gives almost instantly rise to a most beautiful golden rose color, which is exceedingly sensitive, but not very stable. When the formation is continued for a second or two, a deeper violet-red appears which remains practically constant, but the golden hue gradually fades away. The sensitiveness of the cell when filled with the different gases is shown by the curves of Fig. 3. Neon again JAKOB KUNZ AND JOEL STEBBINS. [SECOND [SERIES. shows the greatest sensitiveness, hydrogen the smallest, argon seems to give a curve which lies between A and B, but this question is not quite settled. A comparison of Figs. 2 and 3 shows that for rubidium we find the same photoelectric current with a potential difference about 40 volts smaller than for potassium. Very striking iridescence can be obtained by the potassium. Cells have also been formed with sodium and caesium. The former metal gives very sensitive cells, but their construction is more difficult than that of the potassium and rubidium cells, the sodium seems to act somewhat on the silver mirror, so that the distilled metal does not seem so bright on the silver as on the glass. If however, the metal is distilled on the glass bulb directly, then the contact with the electrode is un- satisfactory. The pure metal seems to give a very sensitive golden toe Fig. 3. layer. The caesium finally is liquid at 28 and can therefore not be used directly. A solid amalgam of this alkali metal has been formed which was, however, of a rather weak sensitiveness. The cells described in this article show a very small dark current; if it exists at all, it can be compensated by the application of a convenient small potential at the platinum cylinder between the two electrodes. As far as our present measurements indicate, there is an accurate pro- portionality between the intensity of the incident light and the photo- electric current. The cells are used in stellar photometry. LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS, August 12, 1915. [Reprinted from the PHYSICAL REVIEW, N.S.. Voi. VII, Nc. i, January, 1916.] AN INVESTIGATION OF THE TRANSMISSION, REFLECTION AND ABSORPTION OF SOUND BY DIFFERENT MATERIALS. BY F. R. WATSON. THE experiments on the transmission of sound were performed with the following arrangement of apparatus. 1 The source of sound was an adjustable whistle blown by air from a constant pressure tank and mounted at the focus of a specially constructed parabolic reflector with a focal length of nine inches and an aperture of five feet. This was placed in front of an open doorway so that the sound, which proceeded in a large parallel bundle from the reflector, could pass through the doorway into another room. The receiver of sound, a Rayleigh resonator, was mounted in the other room in the path of the sound symmetrically opposite the reflector and doorway and measured the intensity of the transmitted sound. The resonator used was a modification of Rayleigh 's original design. 2 It consisted of a horizontal brass tube closed at one end by an adjustable piston. A mica disc was suspended by a quartz fiber at an angle of 45 with the axis of the tube. When the sound of the whistle reached the resonator it set up a back-and-forth surging of the air in the resonator and caused the mica disc, which was placed at a loop, to rotate. This action is in accordance with the general principle that any flat object in a current of air tends to set itself at right angles to the current. The amount of rotation was measured by means of a lamp and scale in con- nection with a mirror which was attached to the suspended system above the mica disc. The readings on the scale are proportional, for small angles of rotation of the disc, to the intensity of the sound. This is shown as follows. The moment M of the couple turning the disc may be proven 3 to be M = kW 2 sin 2(0 - 2 ) / 2 ~

in Fig. 1. When the vacuum is right a beautiful discharge will make its appearance as patches of light on the electrodes. These patches of light, when there is considerable resistance in the circuit and the vacuum is not very high, will be opposite each other and the discharge, as a whole, will wander about, sometimes swinging entirely around, or at times travelling to the edges of the electrodes, only to break away and move to some other point. The movement of the cathode glow (which is the smaller and hence the brighter) is similar to that of the cathode star over the surface of mercury in a mercury 3 vapor lamp. These areas grow as the vacuum improves when ultimately the entire surface of each electrode is covered. Or, with the vacuum kept constant, the areas may be made to increase in size by cutting out resistance. Hence by improving the vacuum and at the same time cutting out resistance the dis- charge, if the inner cylinder is made cathode, grows rapidly into a brilliant bull's-eye. The appearance is very realistic, for if now resist- ance is cut in, the dark space around the cathode (as is evident after a moment's re- flection) grows smaller, and vice versa. Its FIG. 2. outline is exceedingly sharp and perfectly steady, and yet, though the discharge appears very brilliant, the current required may not exceed 20 milliamperes. This form of discharge vessel offers an in- teresting method for the study of the stria- tions and their relative spacing with reference to the impressed discharge potentials. These effects are best shown when the vacuum is not too high and the discharge potential is ad- justed to give a patch on the cathode, which we will take as the inner cylinder, of about one square centimeter in area. Under these conditions the Faraday dark space should be about 8 mm. in length, and the Crookes dark space should be just visible between the vel- vety cathode glow and the cathode electrode. Another prerequisite is that the discharge must not cling to the edge of the aluminum electrodes, but should occupy some intermedi- ate position as shown at 1 in a, Fig. 1. In this position the characteristics of the discharge are shown with exceeding clearness. If now some additional resistance is cut in, the area of the discharge will become less, the Fara- day dark space will shorten, the positive col- umn will move towards the cathode, and the number of striae in it will increase, the extra striae being, as it were, drawn out of the anode. The configuration is perfectly steady except that the discharge, as a whole, is liable to wander. This transition may be continued by a still further increase of the resistance in the circuit, the dark space becoming ever shorter, the positive column lengthening and at the same time shrinking in area and the stria? in- creasing in number, all without loss of out- line or brightness. Finally, the discharge will cease. The various stages are suggested at 1, 2, 3 in l f Fig. 1. In the second method the discharge vessel with its commutator is placed in a derived circuit (Fig. 2). This arrangement enables the discharge potential to be continuously varied over a wide range, and hence for a given vacuum the relation between the length of the dark space and the impressed voltage may be exhibited. Again this arrangement enables the minimum potential to be readily deter- mined that will maintain a discharge. As an example, for a given vacuum with the resist- ance AC equal to 1/3 that of AB the discharge was observed to just pass, indicating that the potential necessary was 330 volts. Additional phases of the experiment will suggest themselves to the operator. CHAS. T. KNIPP LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS, March 4, 1916 [Reprinted from the PHYSICAL REVIEW, N.S., Vol. VII, No. 6, June, 1916.] RETROGRADE RAYS FROM THE COLD CATHODE. BY ORRIN H. SMITH. JJ. THOMSON, 1 as early as 1897, showed that a system of rays of an entirely different character from the cathode rays accompanies the cathode beam. He found that these rays proceed normally from the face of the cathode, that they are not appreciably deflected by a permanent magnet, and that they possess very little, if any, power of producing phosphorescence. In 1906 Villard 2 gave an account before the French Academy of the rays accompanying the cathode beam which are not so readily deflected as the cathode beam but which were deflected in such a direction and by such an amount as would be expected of the "kanal strahlen." He noticed that in a mixture of oxygen and hydrogen (or water vapor) the cathode rays produced a luminescence characteristic of oxygen, but when these were deflected aside by a magnet there remained rays which pro- duced a luminescence characteristic of hydrogen. He explained their presence by saying that they were the positive canal rays which fall against the cathode and rebound. To explain their rebounding beyond the limits of the cathode dark space, he assumed that the potential fall underwent rapid variations or was even discontinuous. A stroboscopic test showed this to be true; however, this was to be expected since he used a transformer to produce the discharge. The following year Thomson 3 showed, independently, that these rays were deflected by strong electric and magnetic fields and that they possessed considerable mass. In a later work he observed that they were very feeble under the most favorable conditions of vacuum, dis- charge potential, etc., and were exceedingly feeble when the gas pressure in the discharge tube was very low. In this latter respect they were quite different from canal or positive rays. Employing a tube having an opening of about .5 mm. in diameter he obtained a photograph which showed that these rays contain (a) positively electrified atoms and mole- cules of hydrogen, (b) positively electrified atoms of oxygen, and (c) negatively electrified atoms of hydrogen and oxygen. The photograph 1 Proc. Camb. Phil. Soc., IX., p. 243, 1897. 1 Comptes Rendus, CXLIIL, p. 673, 1906. * Phil. Mag., XIV., p. 359, 1907. 626 ORRIN H. SMITH. [SECOND [SERIES. showed the intensity of the lines corresponding to the negative ions to be greater than that of the positive ions. With the ordinary positive rays the positive lines are the more intense. The conditions under which retrograde rays are produced are quite different from those that obtain for the ordinary positive rays and for this reason it seemed worth while to repeat and extend Thomson's investigations. Thomson does not find the molecule of oxygen with the negative charge while in this investigation the molecule of oxygen and the molecule of hydrogen are the only carriers obtained with a negative charge, no atoms appearing at all. The presence of helium in the discharge chamber apparently makes no difference in the photographic result. Fig. 1. Top View. MN, containing vessel ot glass; pp, glass end plates; mn, large brass cylinder; m'n r , magnetic field extensions; EE, electrostatic field plates, connections to which are not shown; m"n", plateholder; P, photographic plate mounted on disc d, supported by telescoping cap m'"n"' , and turned by winch w, DD, aluminum diaphragms; and SI. iron shield. It appears that Thomson was unable to use a tube of less than .5 mm. bore, while in this investigation traces were obtained with a tube and set of diaphragms having openings of about .05 mm. thus producing sharp lines on the plate which made possible more accurate measurements. Owing to the short range at which these rays were obtained on the photographic plate, the increased sharpness of the lines, and the re- stricted range of their velocities due to a restricted cathode dark space, it was possible to obtain some evidence on the question as to whether the power of a particle to affect a photographic plate is a function of its No L 6 VIL ] RETROGRADE RAYS FROM THE COLD CATHODE. 62 J velocity, momentum, or kinetic energy. This evidence seems to indicate that it is a function of the kinetic energy and that the mean value is about 7.4 X io~ 9 ergs. The apparatus, shown in Fig. I, and the manipulation is essentially the same as that described by Knipp 1 except that a cold cathode was used instead of the Wehnelt cathode and the discharge was produced by an induction coil. The cathode was just like the anode and similarly placed facing the line of the tube and the diaphragms. A large Leeds induction coil was operated on ten storage cells. The vacuum was maintained with the aid of a large charcoal bulb dipping into liquid air. In general the vacuum improved with sparking. After a few runs it was found that the liquid air could be removed after about ten minutes from starting, and, as the sparking and pumping continued, it co aid be dispensed with altogether. Finally the vacuum was so easily maintained that it was necessary to keep the pump itself turned off for about three fourths of the time. There is a point of interest in connection with the charcoal bulb. It was left on the apparatus for weeks after its use was found unnecessary, remaining all the while at the nearly constant room temperature. The pumps were unable to produce a vacuum of .005 mm. in fully three hours' time when starting from atmospheric pressure, and this was the case whether the bulb was heated for an hour during that time or not. However, if it was pumped to a pressure of one or two mm. and left to stand for ten to fifteen hours then upon starting the pumps a vacuum of .005 mm. could be attained in twenty to thirty minutes. This, strangely, was true even when the vacuum had been let down for a very few minutes and then the pumps started again immediately. The photographic plate used was Seed's Yellow Label lantern slide plate. This plate is very slow and hence produces great contrast which is the thing desired. Thomson 2 points out that the large ions affect only the surface of the film and do not penetrate like the faster moving electrons, into the film. Hence the plate best suited for this work is one that is slow and that has a thin film with a high percentage of silver. The best traces that could be gotten in this investigation were in many instances so thin that they could hardly be seen. They were obscured easily by the slightest fogging. For this reason a fast plate could not be used. Seed's Gilt Edge Number Twenty-seven plate was tried but in every instance fogging obscured the lines. The Double Coated Cramer Crown plate was tried and found to be entirely too sensitive. Some 1 PHYS. REV., XXXIV., p. 215, March, 1912. 2 Thomson, Rays of Positive Electricity, p. 4. 628 ORRIN H. SMITH. experience by another member of the department obviated the necessity of trying the Cramer X-ray plate. As an instance to show that these carriers affect only the surface of the film, the author gently stroked the film under water with a fine camel's hair brush to remove foreign particles and it was found that, in some cases, the lines were entirely obliterated. Further, after the negative had dried the lines could be obliterated by breathing on the film and wiping it gently with a soft cloth. In both cases, other than erasing the lines, no further change could be detected in the film. It was found advantageous to put some alum in the fixing bath to harden the film. The developer used was ordinary hydrochinon, the time of development being from six to twelve minutes. The time of exposure varied from thirty minutes for the small to three hours for the larger deflections. There seems to be a limit to the intensity that is obtainable, for after a certain length of exposure the intensity of the lines did not apparently increase with further exposure. This was true for long or short development or even when they were exceed- ingly dim. This is in agreement, however, with the theory that they affect only the surface of the film. Thomson found that the retrograde rays were best obtained when the gas pressure was not too low. The present photographs bear out that fact very well. If the vacuum was kept about .002 to .004 mm. scarcely any trace of the rays could be found on the plate. The best pressure for their production seems, from this investigation, to be between .015 and .008 mm. There is always a central spot that is undeflected which is probably due to neutral carriers that were negative originally but which lost one electron before they got into the deflecting fields. It would seem from this that a moving particle need not be charged in order to affect a photo- graphic plate. It is quite evident that the velocity of an uncharged particle must be above a certain value otherwise a plate would be affected by exposure to the air in a dark room due to no other agency than to the velocity of the air molecules produced by ordinary heat agitation. The mean of this velocity at o C. for the hydrogen molecule is about 2 X io 5 cm./sec. and for the oxygen molecule about 4.5 X io 4 cm./sec. Whether the ability of a moving particle to affect a photo- graphic plate is due to its momentum or its kinetic energy, or simply to its velocity, is not definitely known. It seems reasonable to expect, however, that it should be a function of one of these. On a number of the plates the lines were distinct enough to locate approximately the place where the slowest ions would strike, i. e., those that had just suffi- cient velocity to affect the plate. These points were found, in every VOL. VII.1 No. 6. RETROGRADE RAYS FROM THE COLD CATHODE. 629 case, to be well within the limits of the field, i. e., so far as the limits of the apparatus are concerned the lines might have extended farther from the origin. It occurred to the author then to assume that there were particles which struck beyond the last points of the visible trace but whose velocity was not sufficient to cause them to affect the film. If the coordinates of the last visible point in each line be measured and v and e/m determined, then, for all such points, we should get a constant, showing whether this minimum effect on the plate is a function of the velocity, the momentum, or of the kinetic energy of the moving ion. Table I. shows values which are proportional to the velocity, momentum, and kinetic energy for the points in question on sixteen different lines. It can be seen that the values for the kinetic energy are nearly constant while the values for the velocity and the momentum are not constant. It thus appears that the power of a particle to affect a photographic film probably depends on its kinetic energy. The mean of these values of the kinetic energy is, from Table I., 7.4 X io~ 9 ergs which is the minimum required. This value would probably be different for an electron because of its size. It is somewhat larger than the energy re- quired to produce an ion which is 1.63 X io~ u ergs. The above value (7.4 X io~ 9 ) was calculated from data obtained from this investigation, except for the value of e, by the formula kinetic energy = i/2-m/e-e-v 2 . -20 The value of e was taken as 1.55 X 10 TABLE I. Photographic Plate. Line. Constant X Velocity. Constant X Momentum. Constant X Kinetic Energy. 75 Upper 6.04 18.36 111.0 76 Upper 6.54 17.99 117.6 76 Lower 1.36 87.18 118.6 85 Upper 6.37 12.50 79.0 85 Lower 1.52 52.50 79.7 86 Upper 6.23 12.71 79.2 86 Lower 1.53 52.48 80.4 87 Upper 7.27 19.40 102.5 87 Lower 1.69 60.50 102.3 88 Lower 1.37 61.70 84.5 94 Upper 5.55 10.71 106.4 94 Lower 1.77 36.28 100.4 95 Upper 7.41 15.03 91.1 95 Lower 1.64 51.50 84.47 96 Upper 6.35 17.70 112.5 96 Lower 1.42 59.36 84.26 630 ORRIN H. SMITH. It can be seen from Table I. that, even though the values of the kinetic energy vary somewhat, the values for a given plate as a rule are more nearly alike. Plate ninety-six furnishes the greatest variation from this rule. It might be reasonable to expect that different emulsion numbers would reveal slightly different kinetic energies required to affect the film. Several emulsion numbers are represented in these data. The photographs taken with the apparatus in the last refinement, while clear and capable of accurate measurement, do not lend themselves to reproduction and hence are omitted. The important dimensions are as follows: Length of electrostatic field 1.10 cm. Length of magnetic field 1.10 cm. Distance from point of emergence to plate 1.58 cm. Length of triangular test coil 1 2.52 cm. Base 63 cm. Number of turns 19. The negative lines show distinctly the parabolic heads which are not in evidence on the positive lines. It was evident from nearly all the plates exposed that the negative carriers are in preponderance over the positive ones. This seems reasonable to expect since the distance to the plate is, for the lower pressures, within the limits of the mean free path and it is necessary to assume that every positive carrier has lost two electrons between the outer limits of the dark space and the deflecting fields. If this is true we should expect that the lines due to the positive carriers would not be as sharp as those due to the negative carriers, the ions being deflected somewhat from their true path in the process of losing an electron. Most of the photographs bear this out. It is somewhat surprising, in consideration of the foregoing, that this pre- ponderance is not greater than the photographs seem to indicate unless the negative ion is more unstable than the positive ion. An additional suggestion in the same line comes from a study of Thomson's photographs of positive rays, in a great many of which the negative counterpart is very weak or cannot be seen at all on the prints when the positive lines are very pronounced. The positive lines do not have the distinct para- bolic head that the negative lines have. They are also broader and more diffuse. Joining the parabolic head to the center is a line due to the secondary rays of Thomson. This is shown particularly in one exposure where the electric field overlapped the magnetic so that the secondary line does not join straight on to the head of the parabola. The data for exposure number eighty-five, are given in Table II. This 1 Thomson, Rays of Positive Electricity, p. 10. VOL. VII.l No. 6. RETROGRADE RAYS FROM THE COLD CATHODE. 631 indicates that the carriers which produced the two lines are the mole- cules of hydrogen and oxygen respectively. The measurements of the coordinates were made with an ordinator composed of a frame to which the plates could be fastened so that there was a movable point above the plate capable of being carried in either of two directions perpendicular to each other by micrometer screws. A Grassot fluxmeter was used to determine the strength of the magnetic field. TABLE II. Photographic Plate Number 85. Measurements for the Upper Line. Position. z in mm. y in mm. v X io- cm./sec. elm X 1Q" 4 Electric Atomic Weight. Carrier. 1 3.34 6.42 6.37 .509 1.97 H 2 2 2.46 5.48 7.39 .504 1.99 " 3 1.88 4.77 8.96 .500 2.00 14 4 1.12 3.51 10.38 .458 2.18 M Measurements for the Lower Line. 1 3.34 1.53 1.52 .029 34.5 3 2 2.46 1.31 1.77 .0288 34.8 H 3 1.88 1.16 2.04 .0296 33.8 " 4 1.12 .84 2.50 .0260 38.5 Time of exposure, 3.25 hours. Gas pressure varied between .008 and .018 mm. Electric deflecting field, 965 volts. Magnet current, 4.25 amperes. A = 8,040, B =267 X 10 9 All the photographs were exposed with residual air in the discharge chamber except number 88. In this instance it contained some helium but no traces appear in the photograph, in fact in no case does anything appear in any of the photographs except the lines due to the molecules of hydrogen and oxygen. In some cases the positive rays are not visible. The data show very well how the velocity varies for the carriers striking at the various points along the parabola, that it decreases with increase of distance from the undeflected spot. The value of v and elm obtained for the smaller values of the electric field are in general less reliable than for those for which the deflection is larger. The "elec- tric atomic weight" of a carrier Thomson 1 has defined as the ratio of m/e for that carrier to m/e for the atom of hydrogen. 1 Phil. Mag., XXI., p. 234, Feb., 1911. 632 ORRIN H. SMITH. It was noticed in connection with these experiments that the dis- charge in the chamber passed more easily with the presence of a transverse magnetic field. Earhart 1 has shown that this is true for a longitudinal field. SUMMARY OF CONCLUSIONS. The results of this investigation may be summarized briefly as follows : 1. When obtaining retrograde rays in residual air the molecule of hydrogen appears on every plate accompanied by a heavier carrier which in most cases is the molecule of oxygen. The velocities obtained by the author are smaller than those obtained by Thomson. This is due to the position of the cathode with reference to the small canal through which the carriers pass, the dark space extending beyond the near end of this tube and hence the carriers not attaining their maximum velocity. 2. The negative lines are clearer and sharper than the positive; prob- ably because of the disturbance to the path of the positive particles in the process of becoming positive. 3. Retrograde rays can be obtained with a canal having a bore of about .05 mm. diameter. The best range of pressures for their production is between .008 and .015 mm. of mercury. 4. The power of a moving particle to affect a photographic plate seems to be a function of its kinetic energy. The minimum required for the heavy carriers is of the order 7.4 X io~ 9 ergs, which is larger than the energy required to produce an ion, however, there is evidence in favor of the view that this value may depend somewhat on the emulsion on the plate. In conclusion I wish to express my thanks to Professor A. P. Carman for the excellent facilities placed at my disposal and to Dr. C. T. Knipp for his interest and help in carrying on the investigation. LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS. 1 PHYS. REV., Feb., 1914. [Reprinted from the PHYSICAL REVIEW, N.S., Vol. VIII, No. i, July, 1916. J AN EXPERIMENTAL VERIFICATION OF THE LAW OF VARI- ATION OF MASS WITH VELOCITY FOR CATHODE RAYS. BY LLOYD T. JONES. INTRODUCTION. HHE mass of the electron has been shown by W. Kaufmann 1 to be -*- electromagnetic in origin. This mass is shown by the elementary laws of electromagnetism to be constant for small velocities of the elec- tron. M. Abraham 2 has developed an electro-dynamic theory of moving electrons by which he accounts for the falling off of the ratio e/m for electrons moving with high velocities. If /3 is the ratio of the velocity of the electron to that of light, the ratio of the mass of the electron moving with the velocity v to its mass, mo, when moving with a slow velocity is m i The Lorentz-Einstein formula, which satisfies the principle of relativity, gives the ratio of the masses as Kunz 3 has discussed the bearing of these formulae in connection with an electromagnetic emission theory of light and has developed three forms of the formula based on possible changes of form of the electron. Stark 4 has found that the mass of the cathode particle increases as the velocity increases. The maximum velocity employed by him, I.I4XIO 10 cm. per sec., was, however, not great enough to cause more than a small per cent, increase in the mass. Later Guye and Ratnsoky 5 carried out an experiment employing rays of 14.7 X io 10 cm. per sec. velocity and obtained an increase of nearly twenty per cent, in the mass. Each of the investigators has employed a method in which the cathode 1 W. Kaufmann, Gott. Nachr., 1901, Heft 2; 1902, Heft 5; Phys. Zeitschr., 4, 54, 1902. 2 M. Abraham, Gott. Nachr., 1902, Heft. i. 8 J. Kunz, Arch, des ScL, Jan. 1913; PHYS. REV., p. 464, 1914. 4 H. Stark, Verh. d. Deut, Phys. Gesell., 5, p. 241, 1903. 6 Guye and Ratnosky, Arch, des Sci., 31, p. 293, 1911. Guye and Lavanchy, Comptes Rendus, p. 52, July, 1915. 53 LLOYD T. JONES. [SECOND [SERIES. beam traverses nonuniform electric and magnetic fields and the deflection is shown on a phosphorescent screen placed perpendicular to the path. This necessitated a homogeneous cathode beam. The conclusions of the experimenter must be based on a large number of observations taken at each of a number of different velocities. The method that has been developed for the present research lessens materially the difficulties encountered in a verification by cathode rays and is applicable equally well for the /3 particles of radium. Perhaps the best feature of the method is that it is desired to have rays of all possible velocities present in the discharge rather than a homogeneous beam. This allows one to use the discharge from a high potential transformer without any additional pieces of apparatus to operate during the time of exposure. Since from a single photograph calculations may be made of e/m for all the velocities present it is possible to obtain the desired results by a single exposure. THE APPARATUS. In a previous determination of e/m and v for cathode rays 1 an apparatus was used involving the same principles as this; the high discharge po- tentials used in the present investigation, however, necessitated a change in the manner of introducing the electrodes and more effective insulation guarding against the ionizing and direct effect of the discharge. Fig. 1. A glass jar 11.5 cm. in diameter and about 35 cm. long had a 2.2 cm. hole bored in its base through which the cathode was introduced. The cathode was an aluminum disc about .8 cm. in diameter carried on a small brass rod encased in a small glass tube and connected with one terminal of the transformer through a platinum wire sealed in the glass. L. T. Jones, PHYS. REV., N.S., Vol. III., p. 317. 19*4- No"i VI11 '] VARIATION OF MASS WITH VELOCITY. 54 The glass tube encasing the cathode rod was supported at two places by a second glass tube sealed, as shown at b in Fig. I, to a tube of 2 cm. diameter which passed through the hole in the base of the jar. This tube was fastened to the base by sealing wax. A brass cylinder, C, of 10.2 cm. diameter and about 32 cm. long was fastened rigidly (manner not shown) to the glass jar; and a brass ring, R, of 1.5 cm. width and .4 cm. thickness was soldered inside it with its plane perpendicular to the axis of the brass cylinder. An iron cylinder, 5, of 7.5 cm. inside diameter and .8 cm. thickness was fastened by screws to the ring R. An ebonite ring, Fj of nearly the same dimensions as R was fastened to R by screws whose heads were sunk well beneath the surface next G. G was a brass disc of .3 cm. thickness fastened by brass screws to the ebonite disc, L, which was of .8 cm. thickness and carried the electrostatic plates. To increase the insulation discs of mica were placed between G and L, F and G and R and F. To prevent trouble due to the heavy discharge a brass disc, M, was held against R by a slip ring in S. A few millimeters' space was left around the small iron tube, /, which passed through di- rectly in front of the cathode. The two electrostatic plates were brass plates 20.5 X 7-5 X 1.2 cm. In the upper one was inlaid a piece of soft iron, N, 5.13 X 1.4 X .1 cm. A similar piece of iron, P, was held against N by eight short iron screws. After the iron piece, N, was inlaid and all necessary holes had been made in the plates they were annealed and then one side of each was surfaced to within .001 cm. of plane. The slip P also had its face next N made plane. A scratch of about .05 cm. width was drawn full length on the plane side of P. The ends of this scratch, for about I mm. of their length, were closed with solder and the solder cut off flush with the sur- face. A small cut was then made in each of the bits of solder and these cuts determined the path of the electron immediately before its entrance into the deflecting fields. The electron then takes the path indicated by the dotted line in Fig. I. The electron is thus protected from the fields until it leaves the constricting canal. Care was taken that the small cut marking the entrance of the electron in the fields was perfect to the ends of N and P and that the ends of N and P were exactly even. As a final precaution a small bit of solder was placed in the middle of the canal as well and a small cut made in it. This insured a straight beam through the tube. Each of these cuts was .01 cm. in width and of about the same depth. The softest iron obtainable was used throughout and the brass was free of magnetic material. The ebonite disc, L, with its plate, G, was held against the ring, F, by four heavy brass screws threaded into R. They were insulated from G by an air space of about 2 mm. 53 LLOYD T. JONES. [SECOND LSERIES. beam traverses nonuniform electric and magnetic fields and the deflection is shown on a phosphorescent screen placed perpendicular to the path. This necessitated a homogeneous cathode beam. The conclusions of the experimenter must be based on a large number of observations taken at each of a number of different velocities. The method that has been developed for the present research lessens materially the difficulties encountered in a verification by cathode rays and is applicable equally well for the /3 particles of radium. Perhaps the best feature of the method is that it is desired to have rays of all possible velocities present in the discharge rather than a homogeneous beam. This allows one to use the discharge from a high potential transformer without any additional pieces of apparatus to operate during the time of exposure. Since from a single photograph calculations may be made of e/m for all the velocities present it is possible to obtain the desired results by a single exposure. THE APPARATUS. In a previous determination of e/m and v for cathode rays 1 an apparatus was used involving the same principles as this; the high discharge po- tentials used in the present investigation, however, necessitated a change in the manner of introducing the electrodes and more effective insulation guarding against the ionizing and direct effect of the discharge. Fig. 1. A glass jar 11.5 cm. in diameter and about 35 cm. long had a 2.2 cm. hole bored in its base through which the cathode was introduced. The cathode was an aluminum disc about .8 cm. in diameter carried on a small brass rod encased in a small glass tube and connected with one terminal of the transformer through a platinum wire sealed in the glass. 1 L. T. Jones, PHYS. REV., N.S., Vol. III., p. 317, 1914. NoTiY 111 '] VARIATION OF MASS WITH VELOCITY. 54 The glass tube encasing the cathode rod was supported at two places by a second glass tube sealed, as shown at b in Fig. I, to a tube of 2 cm. diameter which passed through the hole in the base of the jar. This tube was fastened to the base by sealing wax. A brass cylinder, C, of 10.2 cm. diameter and about 32 cm. long was fastened rigidly (manner not shown) to the glass jar; and a brass ring, R, of 1.5 cm. width and .4 cm. thickness was soldered inside it with its plane perpendicular to the axis of the brass cylinder. An iron cylinder, 6", of 7.5 cm. inside diameter and .8 cm. thickness was fastened by screws to the ring R. An ebonite ring, Fj of nearly the same dimensions as R was fastened to R by screws whose heads were sunk well beneath the surface next G. G was a brass disc of .3 cm. thickness fastened by brass screws to the ebonite disc, L, which was of .8 cm. thickness and carried the electrostatic plates. To increase the insulation discs of mica were placed between G and L, F and G and R and F. To prevent trouble due to the heavy discharge a brass disc, M , was held against R by a slip ring in S. A few millimeters' space was left around the small iron tube, /, which passed through di- rectly in front of the cathode. The two electrostatic plates were brass plates 20.5 X 7.5 X 1.2 cm. In the upper one was inlaid a piece of soft iron, N, 5.13 X 1.4 X .1 cm. A similar piece of iron, P, was held against N by eight short iron screws. After the iron piece, N, was inlaid and all necessary holes had been made in the plates they were annealed and then one side of each was surfaced to within .001 cm. of plane. The slip P also had its face next N made plane. A scratch of about .05 cm. width was drawn full length on the plane side of P. The ends of this scratch, for about I mm. of their length, were closed with solder and the solder cut off flush with the sur- face. A small cut was then made in each of the bits of solder and these cuts determined the path of the electron immediately before its entrance into the deflecting fields. The electron then takes the path indicated by the dotted line in Fig. I. The electron is thus protected from the fields until it leaves the constricting canal. Care was taken that the small cut marking the entrance of the electron in the fields was perfect to the ends of N and P and that the ends of N and P were exactly even. As a final precaution a small bit of solder was placed in the middle of the canal as well and a small cut made in it. This insured a straight beam through the tube. Each of these cuts was .01 cm. in width and of about the same depth. The softest iron obtainable was used throughout and the brass was free of magnetic material. The ebonite disc, L, with its plate, G, was held against the ring, F, by four heavy brass screws threaded into R. They were insulated from G by an air space of about 2 mm. 55 LLOYD T. JONES. The two electrostatic plates were held at a fixed distance apart by four porcelain blocks placed one at each corner. Under the back end of the lower plate was placed a brass leg, Q, of adjustable height which served as an additional support for the plates and at the same time con- nected the lower plate electrically with the brass cylinder, and through it with M and 5. A hole 2.2 cm. in diameter was bored in the side of the glass jar at a suitable position and a glass tube waxed to the jar here connected the vessel to the molecular pump. A wire, A t was connected to the brass cylinder near the back where it could be easily reached from the outside. A was connected to earth and to the second terminal of the transformer. The surfaces of M and S served as anode. The upper of the electrostatic plates was connected electrically to the outside by a wire, B, passing through an insulating plug in the brass cylinder and through a small hole in the glass cylinder. The hole was made vacuum tight by sealing wax. The photographic chamber was made light tight by closing the ends of the cylinder with a brass cap and the jar was made vacuum tight by closing with a glass plate sealed on with a mixture of beeswax and resin. The electrostatic potential was applied to A and B and the transformer connected to A and D. THE SPACING BLOCKS. Each of the four spacing blocks placed between the corners of the electrostatic plates was a length of a porcelain tube of 1.2 cm. external diameter. After the sections had been cut from the tube they were waxed inside a short piece of brass tubing whose outside was accurately round so it could be chucked in the grinding machine. They were ground down till they were of nearly the same length and the end planes parallel. They were then finished by hand on an iron plate with emery till they were very accurately the same length and the end planes parallel as the measurements showed. The length of the blocks was measured by an optical lever of 24.415 cm. length with a scale 3 meters distant. The lengths of the blocks were .9822 .0008 cm. THE ELECTROSTATIC POTENTIAL. A high potential storage battery, T, was used to send a small current through two high resistances, M and R, shown in Fig, 2. M consisted of two Wolff boxes aggregating 2 X io 6 ohms and R was an adjustable resist- ance of io 4 ohms. The potential drop across a part of M was compared by means of the potentiometer, P, with a Weston standard cell of 1.0183 volts at 24 C. The standard cell checked with one recently received No^iY 111 '] VARIATION OF MASS WITH VELOCITY. 56 from the Bureau of Standards. By adjusting R the value was easily kept constant to within I volt and the value thus determined to less than .1 per cent. The two electrostatic plates were connected directly to the terminals of M. Fig. 2. THE MAGNETIC FIELD. The magnetic field was due to a constant current through 240 turns of wire wound on a rectangular wooden frame about 160 X 60 cm. The cross-section of the coil of wire was about 2X2 cm. Calculation showed the field to be uniform over a range greater than that used. The field was calibrated by the aid of a solenoid of 1 ,141 turns and 149.83 cm. length wound uniformly on a wooden frame of aboat 6X9 cm. cross-section. The solenoid was placed in the geometrical center of the rectangular frame so that the fields either coincided or opposed each other. A small coil of about 200 turns of very fine wire wound on an ebonite rectangle 2X8 cm. was then placed in the center of the solenoid. This coil was connected to a Grassot fluxmeter whose scale was about 4 meters distant. A known constant current was sent through the coil to be calibrated and the current through the solenoid adjusted until the fluxmeter showed no deflection when the two currents were broken simultaneously. The ratio of the currents, 70 to 13.55, gave the value of the field to be 1.854 gausses per ampere. A field of .002 gauss pro- duced a deflection of .3 mm. on the fluxmeter scale. THE MEASUREMENT OF THE CURRENT. The current in the magnetic field was measured with a Siemens & Halske ammeter of 150 scale divisions which, with the shunt used, had a range of o to 3 amperes. The ammeter was calibrated by passing a current through it in series with two Hartmann & Braun standard resistances of .1 and i ohm. The potential drop across each resistance was measured by the Wolff potentiometer against the Weston standard cell and the current calculated. The standard resistances were kept in an oil bath at constant temperature. The Reichsanstalt certificates showed the resistances to be sufficiently correct. The calibrations by the two resistances checked. Throughout the calibrations and experiment an adjustable resistance was used to set the ammeter needle exactly on a 57 LLOYD T. JONES. [sS scale mark in order that any variation in the current could be more easily detected. With special care taken for good contacts little dif- ficulty was experienced in keeping the ammeter needle exactly on the division mark. THE VACUUM. The Gaede molecular pump, with the Gaede mercury pump as a pre- liminary, was used for the exhaustion. The molecular pump was con- nected by 30 mm. tubing directly to the vessel to be exhausted with no stopcock or other constriction intervening. The mercury pump was connected to a McLeod gauge and a large tube of cocoanut charcoal. The order of starting the pumps assures freedom of mercury vapor in the discharge tube. The construction of the apparatus with its sealing- wax joints made it quite impossible to heat the vessel to rid it of moisture. Such a proceeding proved unnecessary with the wide connecting tubes used, however, as an hour of pumping was usually sufficient to produce a vacuum that caused the transformer to spark 20 cm. between its point terminals rather than pass through the discharge tube. This degree of rarefaction was usually produced without the aid of liquid air on the charcoal. To be sure the equivalent spark length of the tube always dropped a few centimeters during the time of discharge, but a half or at most one minute of pumping was sufficient to restore the vacuum. It may be of interest to some users of the molecular pump to know that considerable trouble was experienced with the pump due to the creeping in of oil from the bearings. Once in about six weeks the pump became stiff and the half H. P. motor was unable to drive it at the normal speed used, 8,000 R. P. M. The oil was then taken from the bearings and the whole pump thoroughly washed with filtered gasoline and dried by drawing air through it. This operation usually required three days, THE ELECTRIC DISCHARGE. The transformer used to produce the cathode beam was one built for the ratio 110-40,000 volts operating on a 6o-cycle circuit. For a number of photographs it was used on a 44O-volt 6o-cycle circuit. The rays thus produced were of rather a slow velocity although the vacuum was so high that the transformer sparked across a 20 cm. gap between points outside. In order to lessen the amount of energy used and still retain the potential the transformer was operated on no-volts D.C. with a Wehnelt interrupter. This arrangement, with or without a capacity across the interrupter, gave rays of a much higher velocity. Under these conditions, however, the equivalent spark gap of the vacuum was only about 8 to 12 cm. No" i y ] VARIATION OF MASS WITH VELOCITY. 58 THE FORMULA. The beam passes through uniform electrostatic and magnetic fields, whose lines are parallel to each other, and strikes the photographic plate which is lying on the lower electrostatic plate. Let the particle be subjected to the simultaneous action of the electric and magnetic fields. The particle will be bent downward by the electric field and strike the photographic plate at a distance I (measured along the direction of the undeflected beam) from the source. It will at the same time be bent aside by the magnetic field a distance z (measured at right angles to Z) . Since many velocities are present they will show them- selves in a long trace on the photographic plate and e/m may be calculated for any point in the trace and hence for that velocity. If the electro- static field alone acts the resultant trace will be straight down the center of the plate. If the magnetic field also acts, then for each value of the current a trace will appear at the side and, when the current is reversed, a similar trace on the opposite side and at nearly the same distance from the center one. In photograph 58, Plate I., two values of the current were used which, with the central magnetically undeflected exposure, make five traces on the plate. The magnetic deflection, z, was taken as half the distance between two corresponding points of corresponding traces. The electrostatic plates were mounted horizontally. Each particle then describes an arc of a parabola in the vertical plane and an arc of a circle in the horizontal plane. THE ELECTROSTATIC DEFLECTION. Let d be the distance from the upper electrostatic plate to the upper surface of the photographic plate and let t be the thickness of the photo- graphic plate, Fig. 3. If K is the dielectric constant of the photographic k & M Fig. 3. plate and V the potential difference in volts of the two electrostatic plates the force on unit charge due to the electric field is F VXIO? (* d + t/K' This force produces a downward acceleration of the electron such that Ee = ma, (2) 59 LLOYD T. JONES. [SECOND [SERIES. where e is the charge, m the mass and a the acceleration of the electron. If ti is the time required for the electron to fall to the photographic plate we shall have vtl = v// 2 + z 2 , (3) where v is the velocity of the electron. Equation (3) is true, since z is small enough in comparison with / that the chord may be considered equal in length to the arc. Then and, since we get d = d = =X 2 , Ee P + z 2 (4) (5) (6) 2m v 2 Substituting the value of E from equation (i) and rearranging we have mv 2 V(l 2 + 2 2 )io 8 e ~ 2d(d + t/K) ' (7) THE MAGNETIC DEFLECTION. If the plane of the photographic plate be considered as in the plane of this page with the source of cathode rays at the origin, 0, of the set of axes shown in Fig. 4, the arc of the circle shown will be the projection on the photographic plate of the elec- tron's path and will show accurately the curvature of the path due to the magnetic field. Let z be the mag- netic deflections, measured as previously mentioned, and let / again be the x distance to where some electron of velocity v strikes the plate. If r is the radius of cur- vature of the circular path due to the magnetic field, the length of the projection on the photographic plate of the actual path, or the arc shown, will be rB = vh, (8) where is the angle at the center of the circle sub- tended by the arc. From Fig. 4 we see that 4. and that But tan r z (9) (10) VOL. VIII.-J VARIATION OF MASS WITH VELOCITY. 60 No. i. + COS 6 and from Fig. 4 6 I COS 6 tan - = Ji (n) 2 X I cos 6 = -- . (12) Then and 1 = ^' (I4) whence P + z* r=-* (15) The magnetic force on the particle, due to the field H, is perpendicular to the direction of motion of the particle and hence has only its component, Hev cos 0, in the y direction. Since only this component produces the deflection z, we shall find the average force, /, on the particle and use this value for the magnetic force. Hev I cos Odd . . 7 J rr Sin & t ^ /=- -=&. . (16) This force gives the electron an acceleration a\ in the y direction. Then sin 6 (17) and z = \a^. (18) From equations (8) and (18) we have and from (17) e sin 6 "-*' (20) On substitution of the values from (19) and (20) in equation (18) we get e Hr 2 sin z = -- -- . (21) m 2v From Fig. 4 sin = ~ , (22) and, with an approximation, 6 1 LLOYD T. JONES. [lS?E S D + z 2 . (23) Substituting these values in (21) we find z = -N// 2 + s 2 (24) mv 2 or /_-\ ^ = tfv7?T^' From equations (7) and (25) we obtain the desired expressions, X io 8 Hld(d + t/K) and e z 2 V2 X io 8 m ~ HH^d(d + t/K) ' For any single photograph taken with constant deflecting fields equation (27) may be written in the form z = C^e/m, (28) where C is a constant. This equation shows the traces to be straight lines for constant values of e/m and that the outer traces should curve toward the central one for the higher velocities. From the way e/m enters the equation one would expect only slight curvature of the traces unless e/m diminished very rapidly. The equation shows that only the ratio z/l or the slope of the straight lines need be obtained from the photographic plates. This method is thus made one of particular value for the determination of e/mo, for slow velocities, as it permits easy averaging of values. THE EARTH'S FIELD. In fastening the apparatus to the stone pier it was carefully placed so that the undeflected beam travelled horizontally in the direction of the earth's field. The effect of the vertical component of the earth's field was then to increase the one deflection of the magnetic field and to lessen the deflection when the current was reversed. From an inspection of the equation it is seen that the effect of this vertical component may be neglected as it cancels due to the method used in measuring z. The beam of electrons travelled from north to south so that when only the electrostatic field bends it downward it cuts the horizontal component of the earth's field at a small angle. The central trace is thus thrown a little to one side. Let HI be the value of the horizontal component of the earth's field. L ' VI11 ' No L 'i VI11 '] VARIATION OF MASS WITH VELOCITY. 62 When the electron is deflected magnetically it has a component velocity at right angles to the magnetic field HI and therefore has a small force acting on it. This force will aid or oppose the force of the electrostatic field depending on the direction of the magnetic deflection. This small force due to HI was found to be negligible. It follows then that a small error made in placing the apparatus such that the beam would travel neither quite horizontally nor exactly in the magnetic meridian would have no appreciable effect on the results of the experiment. The dielectric constant, K, of the photographic plate was taken as 6. Since the plate is in contact with the lower electrostatic plate and the electrostatic field is on for ten to thirty minutes before the exposures are made the value of the constant chosen must not be that obtained by a method not allowing for the accumulation of a charge by the glass. It should be pointed out, however, that if the value of e/m Q is measured from the same photograph the value of K will in no wise affect the value of the ratio m/wio if only K remain constant. It will enter, however, in the determination of the velocity of the electron but the error thus intro- duced is relatively small. The deflecting magnetic field was kept at values sufficiently small that z 2 could be neglected compared with I 2 . The equation for the velocity then becomes zV X io 8 (29) If the value of e/m is calculated from the smaller deflections, ZQ and / , on a photograph the ratio m/niQ for the higher velocities is given by The individual values of e/m as calculated from the photographs are shown in Fig. 5, in which (as well as in Figs. 6, 7 and 8) the full line curves marked " A " and " L " correspond to the theoretical values of Abraham and Lorentz respectively. Of the points lying above both of these curves all except three are due to a single photograph. The ratio of the masses was also calculated by means of the preceding equation. To test which of the theoretical curves the points collectively best fit it was assumed that the value for the slowest velocity electrons showing on each of the photographs was a value exactly fitting the Lorentz curve and the other values were plotted by using only the ratio of the masses as calculated from the photographs. These values are set down in Fig. 6. Similarly Fig. 7 shows the results assuming the LLOYD T. JONES, fSECOND [SERIES. value for the slowest velocity showing on each of the photographs to lie exactly on the Abraham curve. Now by a comparison of Figs. 6 and 7 it is seen that in either case the points fit the Lorentz curve more nearly than the Abraham curve. .7 9 /.* 1.3 l.S 1.7 J.t Fig. 6. Table I. gives the data and results taken from one pair of traces on one of the photographs. TABLE I. /Cm. 20 Cm. zJtCm. elm X I0 ~ 7 - v X 10-10. Remarks. 3.93 .1443 .01836 1.708 .6089 4.43 .1587 .01791 1.625 .6696 6.93 .2503 .01806 1.653 1.056 Photograph 58, 7.43 .2667 .01795 1.632 1.125 1,926 volts, 7.93 .2817 .01796 1.599 1.189 d = .8137 cm., 8.43 .2957 .01754 1.558 1.247 <*+//# = . 8418 cm. 8.93 .3107 .01740 1.533 1.311 9.43 .3250 .01723 1.504 1.371 9.93 .3427 .01726 1.508 1.446 10.43 .3583 .01718 1.495 1.512 PHYSICAL REVIEW, VOL. VIII., SECOND SERIES. July, 1916. PLATE II. To face page 64. Photograph 63. Photograph 64. Photograph 66. Photograph 68. LLOYD T. JONES. PHYSICAL REVIEW, VOL. VIII., SECOND SERIES. July, 1916. PLATE I. To face page 64. Photograph 54. Photograph 58. Photograph 59. Photograph 60. LLOYD T. JONES. VOL. VIII.l No. i. VARIATION OF MASS WITH VELOCITY. 6 4 Fig. 8 represents graphically the results shown in Table I. On each of the photographs the lines seen crossing the electron paths were drawn between the jaws of a pair of vernier calipers. The photo- graphic plate while in position touched the ebonite disc, L, Fig. I, and hence the length of the iron slip, P, determined the distance of the opening 1.9 Fig. 7. from the end of the photographic plate. On each of the photographs the line near the right is that marking the opening and the others show the successive values of / for which the values of elm and v were calculated. In several of the photographs, 54 for instance, the lines could be seen nicely with the unaided eye but were too dim when seen through the comparator microscope. These lines were touched with a sharp pencil and these marks used to determine the position of the lines. The photographs show very easily which of the lines were so treated. The distance apart of the traces, 22, was measured by a comparator reading to .005 mm. The value of 22 for each distance was measured 65 LLOYD T. JONES. five times, usually on different days, and the average taken. Usually no measurement differed more than .001 cm. from the average and almost never did one differ more than .002 cm. The comparator screw was calibrated. It was found experimentally that the distortion of the magnetic field due to the iron of the constricting canal had the effect of making the mag- netic deflection smaller. It may be considered as zero for a small distance p further and then constant for the remainder of the path. This has the effect of making / smaller and hence e/m and v larger. The length / does not enter directly into the value of v unless the two values of / for the distance of travel in the two fields, electrostatic and magnetic, are different. The value 1.765 X io 7 was assumed as the correct value of e/mo and the two curves in Figs. 5, 6 and 7 accordingly point to this value for slow velocities. The magnitude of the factor p was calculated and this value, p = .07 cm., was used to correct all the values of I used. This correction was assumed to be the same for the electrostatic field. CONCLUSIONS. 1. The method used in the present investigation does not necessitate a homogeneous cathode beam. 2. Each photograph gives a trace of all velocities present and makes possible a verification of the law from a single photograph. 3. The cathode beam never leaves the region between the electrostatic plates. The uncertain field distribution at the ends of the plates is thus avoided. 4. The present investigation has been carried out with rays of a velocity B little greater than any previously employed. 5. The results favor the Lorentz-Einstein rather than the Abraham formula. In conclusion I wish to express my appreciation to Dr. C. T. Knipp for the enthusiasm with which he has followed the progress of the work. Also I wish to express my thanks to Prof. A. P. Carman, director of the laboratory, for the facilities he so kindly placed at my disposal. LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS, March i, 1916. [Reprinted from the PHYSICAL REVIEW, N.S., Vol. VIII, No. i, July, 1916. J ON THE INITIAL CONDITION OF THE CORONA DISCHARGE. BY JAKOB KUNZ. r I ^HE glow discharge of electricity surrounding the transmission wires under the influence of high potential differences has been studied by electrical engineers of England and America in recent years. In the majority of these investigations alternating current has been used, and very definite empirical results have been obtained. Comparatively few researches have been carried out on the direct corona, among which those of Watson, Schaffers and S. P. Farwell 1 may be mentioned. Farwell especially has shown that the phenomena are far more complicated than what has been revealed by the use of alternating potentials. Before making an attempt at an explanation of some of the phenomena I wish to describe briefly the various forms of the corona due to direct current potentials. There is hardly another electric phenomenon which shows the difference between positive and negative electricity in so many different ways as the corona. There are electric, optical and mechanical differences. For very small wires the negative glow appears before the positive, for larger sizes the positive glow appears before the negative. The boundary between the two regions is a diameter of about 0.075 mm. The positive corona in air forms a very even uniform layer of light of practically constant thickness. The negative corona on the other hand starts also in a uniform layer of red light, but very quickly breaks up into bright beads, separated from each other by dark intervals. Especially at lower pressures this difference between positive and negative polarity is very conspicuous. The negative beads distribute themselves in nearly equal intervals and are fairly stable, so that they can be photographed readily. The positive discharge from the wire in a coaxial cylinder has never been found to break up into beads, but if the discharge takes place between two parallel wires, then at higher potentials the positive column of light also breaks up into shorter intervals and finally into beads. The question arises as to whether the beads are connected with irregularities on the surface of the wire, or whether it is an intrinsic phenomenon, inde- pendent of the surface irregularities. The number of beads depends on 1 Watson, Electrician, London, Vol. 63, p. 828, 1909; Vol. 64, p. 707 and 776, 1909-10. Schaffers, Comptes rendus, July, 1913, p. 203. S. P. Farwell, Transactions of American Institute of Electrical Engineers, Nov. 13, 1914. 2 9 JAKOB KUNZ. the pressure of the gas and on the potential difference. If these two variables are kept constant, the number of beads remains constant, indicating that the beads on smooth wire are an intrinsic phenomenon of the negative discharge. In addition special experiments have been performed with polished and chemically corroded silver wires in order to test this conclusion. For a given potential difference the corona current increases with decreasing diameter of the wire, and with decreasing pres- sure. The characteristic curve, like the starting point of the corona, depends on the polarity and diameter of the wire. For wire smaller than 0.077 mm. diameter the current from the negative wire is greater than that from the positive wire. For the diameter of 0.077 mm - the currents for opposite polarity coincide accurately over a certain range of voltages above the critical voltage, and then the negative current becomes and remains the larger. For sizes of wire larger than 0.077 mm - the curves for the two signs cross each other. For the lower potential differences the positive current is the greater, and for higher potential differences the negative current is the greater. Previous investigators already found that the relation between the electric force E at the surface of the wire and the radius RI is given by the formula where E Q and b are constants, E is calculated by the electrostatic formula: E- -^ AF being the potential difference between the central wire and the cylinder of radius R%. For the smallest sizes of wires used, the relation between E and RI ceases to hold as can be seen from Table I. The critical voltage required to produce visible corona depends not only on the radius of the wire, but also on the pressure. At very low pressures the negative corona starts before the positive one, at higher pressures the positive corona starts at first. The characteristic curves also depend on the pressure. The pressure of the gas and the radius of the wire play an analogous r61e, very thin wires seem to correspond to low pressures. The relation between the pressure p of air, the radius RI of the central wire and the critical electric force E at the surface of the wire is given as follows: VOL. VIII.l No. i. INITIAL CONDITION OF THE CORONA DISCHARGE. where E Q and b are constants. This relation holds as far down as 53 mm. Hg pressure for the positive corona: the constants and b have different values for the positive and negative wire. TABLE I. y? cm. jK+Volts. jE+Volts per cm. +Calcul. y Volts/ E Volts per cm. E Calcul. 0.00135 2,720 2.74X10 5 2.62 2,520 2.52 X10 5 2.55 0.00218 3,380 2.58 2.29 3,230 2.45 2.23 0.0023 3,500 2.25 2.09 3,300 2.08 2.04 0.00258 3,630 2.12 1.99 3,500 2.02 1.94 0.00386 4,060 1.66 1.67 4,060 1.66 1.65 0.00678 5,140 1.31 1.34 5,320 1.36 1.33 0.00825 5,710 1.25 1.25 6,140 1.21 1.21 0.012 6,600 1.07 1.09 6,840 1.09 1.09 0.013 7,180 1.07 1.06 7,660 1.14 1.06 0.0205 8,900 0.93 0.91 9,370 0.99 0.92 0.0325 10,880 0.80 0.79 11,440 0.83 0.80 0.0385 11,850 0.77 0.75 12,400 0.79 0.76 0.0512 13,500 0.71 0.69 14,120 0.73 0.71 0.0642 14,700 0.65 0.65 15,220 0.64 0.64 When the corona starts, the pressure of the gas increases suddenly. We shall call this pressure ionization pressure. It can easily be measured by means of a sensitive U-tube open manometer. This increase of the pressure is very distinctly different from the increase of the pressure due to the evolution of Joule's heat. As soon as the current is interrupted the ionization pressure sinks suddenly down to zero, while the other pressure increases and dies out gradually. The ionization pressure is in general for a given potential difference larger when the wire is negative than when it is positive, but the difference is very small, if not opposite at the be- ginning of the corona. The ionization pressure is very nearly proportional to the current, especially when the wire is positive. The ionization pressure as well as the fact that a higher potential difference is necessary to start the corona for thicker wires can be used with advantage for the construction of voltmeters, some of which are in use in the laboratory of the University of Illinois. It has been mentioned that the negative electricity leaves the wire in the form of very beautiful beads or brushes, mostly evenly spaced along the wire. The number of brushes per unit length depends on the pres- sure and on the potential difference. With increasing pressure and with increasing potential difference the number of beads per unit length in- creases and their brightness at the same time decreases. The beads start from a point of the wire and spread out fanlike in a plane at right 31 JAKOB KUNZ. angles to the wire. Very interesting is the influence of a short arc in series with the tube upon the character of the positive and negative dis- charges. The very well defined positive layer of light spreads out con- siderably and the negative brushes disappear almost entirely, giving room to a continuous glow, whose boundary is ill defined; in other words, a very short spark in series with the discharge tube destroys the difference in the appearance between the positive and the negative corona. This is due to the superposition of a high frequency alternating or intermittent current. A small change of the spark length between the corona and the dynamos produces very marked differences in the luminous discharge. For a certain spark length the corona assumed the form of bright streamers which fill the entire space between the wire and the cylinder. If the spark length is slightly changed, these streamers concentrate into a few luminous bands, about equally spaced, whirling round the wire and pre- senting a very beautiful aspect. If the potential difference is slightly increased, this phenomenon is replaced by the arc, which is apparently the more stable form of discharge. With the introduction of a spark a hissing sound will be heard from the corona tube. The difference between positive and negative elctricity makes itself felt finally in mechanical effects. When the corona takes place between two parallel wires which are not stretched too strongly, the negative wire bows in toward the positive and the positive bows away from the negative. When the wires are purposely made rather slack the positive wire vibrates strongly with a circular motion, while the negative wire remains motionless. The field between two parallel wires and between a cylinder and a coaxial wire has been explored by means of a third platinum electrode. Even before the corona started there was found a distortion of the electrostatic field especially in the neighborhood of the electrodes; and in many if not in all cases the electric force at the surface of the wires is different from the calculated value in the moment when the corona arises. The observed electric force seems to be larger than that calculated from the electrostatic formula. When the field is studied in the space between the central wire and the coaxial cylinder, it becomes very difficult to explore the neighborhood of the negative wire, where the potential seems to be subject to continuous changes. The exploration of the field around the positive wire offers no difficulties. The explanation of the large variety of phenomena described is far from being complete. An attempt at an explanation of some of the phenomena will be made. One might expect that luminous discharge begins when the electric force or polarization on the surface of the wire VoL.JIII.j INITIAL CONDITION OF THE CORONA DISCHARGE. 32 obtains a constant value required for the ionization of the molecules. It has been found however that the critical electric force is given by the expression : Various values for E and b have been given, for instance, E = 30, b = 9 by Y. S. Townsend. Farwell found that the values of E Q and b are distinctly different for positive and negative wires. For positive wires he found E = 31.6; b = 8.43. For negative wires E = 35.0; b = 8.06. We shall now assume that in the neighborhood of the wire in a layer of constant thickness 8. a certain constant energy is required for the beginning corona, different for positive and negative electricity; indeed the splitting up of the molecules into ions and the emission of light requires energy. When a sufficient amount of energy is supplied, the luminous discharge called corona will occur. It has been shown by Schaffers that the thickness 8 = 0.07 cm. of the luminous layer is inde- pendent of the radius of the wire. In the neighborhood of the wire, the electric force E assumes large values so that the polarization also is large and an opposing electric force o will be created, so that the resultant electric force is equal to E E . If k is the dielectric constant, RI the radius of the wire, then we have: E tt = ~27rR l 8(E - E ) 2 , If Eg, k and 5 remain constant, then we have '" i the rule established by the engineers. E , E g and 8 are obviously different for the two polarities of the wire. In favor of this theory is the phe- nomenon of beads. When a thin film of liquid is formed along a thin thread, the film on account of the surface tension breaks up into beads; similarly when a layer of electric energy is formed on the surface of the wire, it will have the tendency of breaking up into beads extending further away from the wire than the original layer. The fact that the negative discharge is much more apt to form beads than the positive one, seems to be connected with the mechanism of the discharge itself. When the wire is very thin negative electricity escapes easier than the positive one, just as in the case of very sharp points and at very low pressures. 33 JAKOB KUNZ. The negative electricity seems to escape both from the molecules of the gas and of the metal, while the positive electricity consists only of positive ions, formed in the air alone, as no positive ions escape from the metal. The positive current consists of positive ions alone, the negative current of negative ions and electrons. Now it seems easier for the electrons to escape in a few places from the metal in large quantities, than from the entire surface of the wire in smaller quantities. That electrons escape from the neighborhood of the negative wire is also indicated by the fact that the negative wire bows in toward the positive one, which bows away from the negative one and that under the same circumstances the negative wire remains almost motionless while the same wire, when charged positively, carries out rotations of large amplitude. For very small wires as well as for low pressures the negative corona starts before the positive one; for larger wires and higher pressures the positive corona starts before the negative. The negative electricity seems to escape in the form of electrons easier from thin metal wires than from molecules of the air. This phenomenon suggests that the average mass of the ions from small negative wires is smaller and the mobility larger than from larger negative wires. Y. S. Townsend 2 has given another theory of the initial conditions of the glow discharge from wires, where he assumes the same values of the constants E and b ; and applies the same theory to the corona as to the spark discharge. The two phenomena are however in many respects different. The law for ionization of a gas by collision can be expressed as follows : -=/(-) . P J \pr Y. S. Townsend made an interesting application of this rule, based on experiments at low pressures, to the corona and spark discharge, which phenomena he considers as due entirely to the same process of ionization. Let us choose the following relations between the two cylinders in which Fig. 1. the corona occurs, 1 Y. S. Townsend, The Electrician, June 6, 1913, p. 348. No L 'i VIIL ] INITIAL CONDITION OF THE CORONA DISCHARGE. 34 ds = zds', z being a given constant number. V = A V is equal to the potential differ- ence applied in both cases: p V p , _ V E, ' 7? ' "~ 7? ~" z * & log *!' log ^ ! log =i -Kl Xti AI E 2 = 1/2 holds not only on the surface of the inner wire but in any two corresponding points such as A and A' or B and B'. The number of ions formed by collision when a negative ion travels over the distance AB = ds is given by: = pdsf(~). P The number of ions produced in the second experiment over the distance ds' is given by: z E l / ? \ a'ds' -AMf.l j~) = ads > a negative ion traveling through the distance ds produces the same effect as over the distance ds' . The same holds for the collision of positive ions. fids = fids', hence we have the same effects in both tubes. A given potential differ- ence V causes the same phenomena in both tubes. If V is sufficient to start corona in one cylinder, it will also give rise to it in the other cylinder. If P Rzp' = zR% ~ R-2,P\ if Ri'P' = RiP and if V= V then RI'EI = EiRi. Rip is therefore only a function of RiEi. If we keep RiEi constant, Rip remains constant. 35 JAKOB KUNZ. [SECOND [SERIES. This theory applies to the beginning spark as well as to the beginning glow discharge. It does not give an answer to one of the first questions regarding the corona discharge, namely, is the current due to ionization by negative or positive, or to both ions? Now the following relation holds between the critical electric force EI and the radius RI or =L , ^ RI bR l - i for p = But if we keep RI - I - = Rip = constant, then E^i remains constant. h~R,o- (6) Then by the law of the conservation of energy, the work required to change a system from one state to another is independent of the path, we have &U + Wi - vodpi = AC/' + W* - v Q dp Q (7) or AC/ - AC/' + Wi - W, = v Q (dpi - dp*). (8) Subtracting (5) from (i) we have At/ - AC/' + Wi - W, = e(i - i'). (9) Therefore e(i - i') = v Q (dpi - dpo). (10) But i = i' + di. Then edi = v<>d(pi - p Q ) (ii) 288 and integrating EARLE H. WARNER. = ~ (Pi Po) a constant. [SECOND [SERIES. (12) Since (pi p Q ) represents the increase in pressure, that is, the ioniza- tion pressure, this equation shows that the ionization pressure should be exactly proportional to the corona current. It was the object of the experiments which have been performed to test this relationship with pure gases in the tube. APPARATUS. The constant potentials were obtained from a battery of continuous current shunt-wound 5OO-volt generators connected in series. The corona tube was of the wire and coaxial cylinder type. (See Fig. Fig. 3. 3.) Glass plates with holes for the wire to pass through were sealed to the ends of the tube so that the holes were on the axis of the cylinder. The wire, No. 32, copper, passed through the holes and was thus coin- cident with the axis of the cylinder. The wire was sealed into these holes and held taut by red sealing wax. To the cylinder was soldered a small " T " tube, one side of which was joined to the vacuum pump and the other side was connected to a Bristol aneroid pressure gauge. The increase in pressure was measured by this Bristol gauge. Any increase in pressure caused it to bend slightly and so rotate the mirror. By observing the deflection of a beam of light over a scale, which had VOL. VIII. No. 3. CONSTANT POTENTIALS. 289 previously been calibrated by reading simultaneously the deflected beam and a water manometer connected directly to the gauge, the increase in pressure in cm. of water could be determined. The advantage of such a pressure measuring instrument in this experiment is that it is very quick in its action. The instant the pressure increases the gauge jumps right up to its new position and a reading can be taken in a very few seconds. It was necessary to read this pressure increase quickly because if much time was required, the heating effect of the current would increase the pressure also. The current was measured by a Type H D' Arson val galvanometer. The apparatus was connected as is shown in Fig. 4. Machine Terminal*. Fig. 4. DISCUSSION. Experiments were made when the wire was positive and the case grounded with dry air, hydrogen, nitrogen, carbon dioxide, oxygen and ammonia as the gases in the tube. Considerable care was taken to see that these gases were absolutely pure. They were all dried carefully before they were used. The following curves (Figs. 5, 6, 7, 8, 9) show graphically the results. Fig. 10 shows all the curves plotted to the same scale. With this scale the hydrogen curve should be continued until its ordinate is equal to that of the carbon dioxide curve. The fact that the points all lie so accurately on a straight line shows conclusively that experiment verifies the prediction made by Dr. Kunz's theory. The law can then be stated that, in the gases studied with the 290 4; EARLE H. WARNER. [iSiEs Relation Between J , IOHIZATIOH PHBSSURB and CORQHA CURRBHT. / I 3 8 c Hydrogen. Wire +. X / x ^ Increase of Pressure 1 N > r" x / X I 2. 3 A 5 6 7 i 10 fl 1 I Current la 10"* Amperes. Fig. 5. wire positive the ionization pressure is exactly proportional to the corona current. In the case of oxygen a considerable amount of ozone was formed due to the corona discharge. Evidently the curve as shown is a resultant of two effects: (i) A chemical change due to the formation of ozone. This would tend to cause a decrease in pressure. (2) The increase in a Relation Between > 8. IOXIZATIOK PRB3SURB and COROTA CURRBBT. ts Hitrogen Wire +. X / X r /x * r > ' X 0* ^x^ 5 f! X ' 3 S 3 _x jS^ x ! X i ,. p/ x / I a 2.0. 3Q 40 -5Q 60 70. SO. 30. 1 00 110. IZO. 130 Current In 1Q-* Amperee. Fig. 6. VOL. VIII.l No. 3. CONSTANT POTENTIALS. 2 9 I Relation Between IOTIZATIOH PRBSSURB and CORONA CURRXHT. Carbon Dioxide. Wire +. IZ. 13 14. lo 4- 5 67 O 9 10 I ( \, Current in 10' Amperes. Fig. 7. pressure due to the ionization of the oxygen. Since the ionization curve is a straight line, as is shown by the gases in which probably there is no chemical action, and since this resultant curve of oxygen is a straight line, the following law can be stated : Whenever chemical change takes place due to the corona the chemical change is exactly proportional to the current. Relation Between \ IOHIZATIOH PRBSSURB and CORONA CURKSHT. jT^ s 3 i h Oxygen. Tire +. / S of Preaaur* in Cm o N / / , / I ' / / 5 Current in LO* 8 'Ampere*. L. 2.5 Fig. 8. 292 EARLE H. WARNER. [SECOND [SERIES. B * 2. 3 5 L5 g M Relation Between IONIZAT10N PRESSURE and CORONA CURRBHT. Ammonia. Wire *. . / ^ ^ X 2r X X 25 J T5 1. 1.2.5 1.5 l.*75 2.0 Current in 10" 8 Amperee. Fig. 9. With the wire negative beads always appear on the wire, and since the pressure increase varies with the arrangement of the beads which are not stable, it is impossible to accurately verify the above relationship. When, instead of the quick acting gauge, an ordinary open manometer which is slow in its action was used, it was discovered that the same relationship as above stated is very nearly true for the wire negative as well as positive. The increase in pressure in the case of nitrogen, showing ionization, is one of the exceptional cases where nitrogen is largely ionized at low temperatures and thus probably chemically active. How nitrogen, carbon dioxide and ammonia are ionized, are questions which require further study. The arrangement of the apparatus could be used as a high potential voltmeter by simply calibrating the increase in pressure against volts, as determined by a disc electrometer. : 3 i i, i . Relation Between I05IZA7IOH PRESSURE and CORONA CURRENT. Wire +. Fig. 10. Na" 3 VI11 '] CONSTANT POTENTIALS. 293 SUMMARY. The ionization pressure in the positive corona is exactly proportional to the corona current in dry air, hydrogen, nitrogen, carbon dioxide, oxygen and ammonia. Any chemical action that takes place due to the corona is exactly pro- portional to the corona current. The writer wishes to acknowledge his indebtedness to Professor A. P. Carman and to Dr. Jakob Kunz, associate professor of physics, for their deep interest and helpful suggestions concerning the conduct of this work. LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS, May, 1916. DIRECT CURRENT CORONA FROM DIFFERENT SURFACES AND METALS. [Reprinted from the PHYSICAL REVIEW, N.S.. Vol. VIII, No. 4. October, DIRECT CURRENT CORONA FROM DIFFERENT SURFACES AND METALS. BY SYLVAN J. CROCKER. I. INTRODUCTION. IT has been shown by F. W. Peek 1 and by S. P. Farwell 2 that the corona discharge is quite different when the wire is positive and when it is negative. The starting point of the corona as well as the characteristic curves depend on the polarity of the wire. When the wire is negative the corona assumes the form of bright " beads " which are strung along the wire more or less evenly, the number of the beads per unit length depending on the pressure of the gas and the potential difference between the wire and the cylinder. This beautiful but complicated phenomenon suggested that probably the surface conditions and the chemical nature of the wire might influence at least the negative corona in the form of beads. It became the purpose of these experiments then to find out the in- fluence of the surface condition of the wire upon the starting point and the characteristics of the corona discharge phenomena. The apparatus used consisted of a metal cylinder (inside diameter 3.63 cm.), with a longitudinal slot for observation (1.53 cm. wide), sealed in a glass cylinder and arranged in such a manner that wires of different sizes could be easily strung along the cylinder axis. It was possible to readily connect the tube to a vacuum pump for varying the pressure. The high potential direct current was taken from forty 500- volt D.C. generators connected in series. The machines were self-exciting and could be cut in or out by closing or opening the field switches. Smaller variations than 500 volts could be obtained by varying the speed of the driving motors or by the adjustment of a rheostat which was connected in the field of one of the machines. The voltage was read on a Kelvin electrostatic voltmeter which had been calibrated with an attracted-disc electrometer. The current was measured with a D' Arson val galvanometer whose figure of merit was found to be 6.25 X io~ 6 amperes. 1 F. W. Peek, Jr., Dielectric Phenomena in High Voltage Engineering, p. 27. 2 S. P. Farwell, "The Corona Produced by Continuous Potentials," A. I. E. E., November 13. 8*8 JZ a 5 rt o a a a a a a a a a a a a cc eg "o "o "o 000 CO CO 00 00 ~o "o "o 0000 O ro O ^ >i a cT) 6 a a a a a a 0) C QJ aJ j3 5 3 ^ e bi) oo ooo > > > ooo ooo ! 1 r + .- S! g S 1 o o o 55 fc S5 DIRECT CURRENT CORONA. 345 No. 4. Preliminary Experiments. Preliminary experiments were made using a steel wire the surface of which was polished over one half its length and corroded with nitric acid over the other half. When the wire was placed in the tube and corona made to form on it at low pressures, the effect of the surface condition was made evident at once. Nos. I and 3 in Fig. I show this experiment. The right half of the wire is polished and has the characteristic negative beads, while the left half is chemically corroded and only a soft glow appears there. This glow is different from the characteristic positive glow in that it is much greater in diameter and has a fuzzy appearance like eider down. Of course it must be noted here that this condition is for a slightly higher potential than that at which the glow first appears and that the fuzzy glow eventually breaks into the beads upon raising the potential. However the beads on the corroded end do not have the sharp clear-cut appearance as those on the polished end, but are fuzzy and less well defined. The positive glow is also shown in Fig. I, No. 2, under these same conditions, but it presents the same appearance for both parts of the wire. The first experiment led to the trial of a wire whose surface was not only (i) polished and (2) corroded, but also (3) mechanically abrased. The differences existing here were also very striking and clearly shown at once. Fig. 2 contains photographs of the negative wire, the left end being abrased, the center polished, and the right end chemically corroded. No. 4 shows the starting of the corona at low pressures and corre- spondingly low voltages. It will be seen that the beads start first on the polished surface (i), while the corroded surface (2) shows no glow and the abrased surface (3) has but a slight brush discharge on it. The beads on (i) are very large, clear, steady and quite evenly spaced. No. 5 shows the effect of a slight increase in voltage where the glow now appears on surface (2) and the beads begin to form on surface (3). Gradually increasing the voltage and the pressure as well causes the glow to become brighter on (2), the beads to increase on (i) and (3). The beads on the abrased portion have a lateral movement, while those on the polished part are still very steady and clear. With still greater increase in pressure and voltage it is possible to reach a condition where the whole length of the wire is covered with clear, steady and evenly spaced beads (see No. 6). Here it seems that the surfaces all act very nearly the same regarding the formation and building up of the corona discharge. Now when the pressure is increased to 370 mm. and the voltage is increased to produce the discharge it is found that the corona starts first 346 SYLVAN J. CROOKER. [ SECOND SERIES. on the abrased portion and that it is only on this part clear steady beads can be obtained (see No. 8). The beads on the corroded part are fairly well defined but they are in an agitated state, moving back and forth on the wire. Under these conditions it is found impossible to get steady beads on the polished part of the wire; instead of the clear beads there is a rather knobby glow on the wire, the condensations in which seem to be beads trying to form. This reversal of the phenomena, as shown in Fig. 2, where the clear beads form on the polished surface at low pressures and on the abrased surface at high pressures, has been found to be a real one for steel wire. The corona starts first on the polished wire for low pressures and begins on the abrased or corroded wire at much lower potentials for high pres- sures. An enameled german silver wire was fitted in the tube after one half of its length had been freed from the enamel and polished. At low pressures for the positive wire the characteristic glow would appear on the polished end. The enameled end would have several small star- like spots of light irregularly distributed over it appearing at points where the insulation had broken down. Keeping the wire positive and increasing the voltage caused very bright " streamers " of purple light to shoot out from a few of these small stars. At higher pressure and higher Tube Purple Streamers v Brig/it Spot on Wire Section Elevation Fig. 4. voltage these streamers increased greatly in number, the glow spreading out into a thin fan-shape. This fan would slowly oscillate or rock back and forth about the bright spot on the wire as a center. Between these fans a hazy fog-like glow was everywhere present. Upon placing an arc in series with the wire and the tube this fog would disappear and the fans would become more sharply defined and more steady. For the wire negative (see Fig. 3, No. 14) it was impossible under any conditions to get the characteristic negative beads. Neither could a glow be produced on the polished end, the only discharge present was on the enameled end similar in appearance to the small stars for the positive wire. However for the negative wire the stars were intensely bright and in slight movement. Fig. 3 shows the appearance of the discharge from the enameled wire when both positive and negative. Fig. 4 gives DIRECT CURRENT CORONA. 347 details of the structure of the positive purple fans. For the enameled wire negative the starting potential was much lower than for the opposite polarity. Figs. I and 3 suggest that the starting point of the corona and the characteristic curves depend on the surface conditions. In order to test this suggestion the following experiments have been performed. II. VISUAL CORONA AND STARTING POTENTIALS. Many characteristic curves were obtained for different sizes of copper wire where the surfaces were polished and abrased and many more char- acteristic curves were taken, using wires of copper, steel, aluminum, and silver where the surfaces were polished, abrased or roughened, and chemically corroded or oxidized. The more striking results will be given in the following paragraphs. Preparation of Surfaces. For the polished surfaces care was taken in choosing wires without kinks or surface scratches. These wires were polished with fine emery cloth and finished with chamois and jeweler's rouge just before placing in the tube. The abrased surfaces were prepared by rolling the wire in emery powder between two hard plane surfaces. Care was taken to have the surface abrased uniformly over the whole length. The corroded surfaces were prepared by different methods. The surface of the steel wire was corroded by dipping in a solution of nitric acid, a black surface resulting. The aluminum wire was corroded by allowing it to remain in a solution of sulphuric acid for a few days. The result was a thin white coating. For copper it was necessary to oxidize the surface by passing a heating current through the wire in the presence of oxygen. Since large quantities of ozone are produced by the corona discharge the silver wire was coated with a layer of silver peroxide by allowing the corona to play on the wire for some time. The phenomena are very complicated. Their description will be carried out according to the surface condition of the wire, and for each individual condition three pressures will be considered. Wires Polished. The general appearance of the corona is the same for all polished positive wires, and differs but slightly for negative wires at the different pressures. At pressures of about 50 mm. when the po- tential is brought up to the glow potential, wire positive, a very faint flashing glow is seen over the whole length of the wire, which becomes uni- form and steady as the potential is raised slightly. The potential may be carried up to the arcing point without changing the general appearance of the uniform glow. The only noticeable change is an increase in the brightness of the bluish glow. SYLVAN J. CROOKER. ("SECOND [SERIES. For pressures of 50 mm. and negative wire, the first appearance of the corona is a flashing glow, similar to that for positive wire, but of much greater diameter and brighter. Increasing the potential causes this glow to remain steady on the wire, becoming uniform and very bright. Very little current flows until a stage is reached not far above the starting point, where the bright uniform glow breaks into large clear character- istic negative beads. From this point on the current increases rapidly with the potential. As the potential is increased the beads increase in number but remain large and well defined, this will be discussed more fully later on. For the polished surfaces and pressure of 50 mm. the negative corona on copper begins at a lower potential than the positive. Corona appears at the same potential for both polarities in the case of steel, but for alu- minum and silver the positive glow begins at the lower potential. This TABLE I. COMPARISON OF STARTING VOLTAGES FOR DIFFERENT SURFACES AND WIRES. All wires about 0.41 mm. diameter. Copper. Polished Abrased Corroded Press. mm. Wire ~ Volts. H Press, mm. Wire ~~ Volts. Press, mm. Wire Volts. 50 252 731 1,700 2,650 6,010 1,780 2,600 5,760 53.2 253 743 1,680 2,550 5,600 1,820 2,800 6,200 50.3 250 1,650 2,010 1,660 2,500 Steel 51.6 1,710 1,710 52.2 1,690 1,740 52.3 1,750 1,700 252.4 2,600 2,600 253.2 2,770 2,770 252 2,550 2,710 727.6 5,660 5,960 736 4,560 5,830 739.4 4,810 5,760 Aluminum. 50 1,760 1,720 52 1,660 1,800 51.9 1,240 1,690 251 2,820 2,900 251.5 2,490 2,900 252 2370 2,66u 74L1 5,880 6,180 741 5,010 5,800 745.3 4,680 5,880 Silver. 53.2 1,850 1,820 52.3 1,730 1,740 52.5 1,850 1,780 252.1 3,150 3,050 252.2 2,600 2,900 252.2 3,150 3,000 744.8 4,210 6,130 743.2 5,060 5,850 746 5,760 6,320 is shown by Table I., which contains the starting potentials for the dif- ferent metals and different surface conditions. Table I. shows no general law. With the exception of the silver wire at a pressure of 746 DIRECT CURRENT CORONA. 349 mm. the starting potential for the corroded wire is smaller for both polarities than for the polished wire. For the negative abrased wire the starting point is in general lower than for the polished wire with only two small exceptions. With the exception of silver the starting point of the abrased positive wire is higher than that of the polished wire. With increasing pressure the differences involved by abrasion and corrosion diminish. The largest influence is found for aluminum wire, negative corroded at 51 mm. For pressures of about 250 mm. the glow for wires positive is the same as before, being uniform and increasing in brightness as the potential increases. For wires negative and polished it was almost impossible to break the glow up into clear-cut beads at this pressure. With in- creasing potential the glow would become brighter and would condense at certain ill-defined points apparently attempting to form beads, but these condensed regions would be in rapid motion back and forth along the wire. For atmospheric pressure, wires polished and positive, the glow would appear faint but uniform and would increase in brightness as the potential was increased. For negative wires a faint flashing glow would appear at break-down potentials increasing in brightness with the potential increase. A very few scattered beads would at times be formed, but they would be small and unstable having very rapid lateral motion. This motion would increase in amplitude and speed with increasing voltage. Clear cut beads over the whole wire was impossible here as in the last case. Wires Mechanically Abrased. With wire surfaces mechanically abrased or roughened and pressure of 50 mm. the positive glow begins with faint flashes as in the case of the polished surfaces, the glow becoming steady, uniform and increasing in brightness as the potential is increased. The starting glow voltage is in general higher than for the positive polished wires, and is also higher than for the abrased negative wires. For wires abrased and negative the corona begins with bright flashes of a fuzzy glow, part of which might have one or two large flashing beads. This flashing glow seemed to pulsate in synchronism with the impulses of the driving machinery. A slight potential increase above the first noticeable glow would cause the glow to break into well-defined beads which would soon become steady and clear, increasing in number with a potential increase. The negative starting voltage for abrased wires is lower than for the polished surfaces. For wires abrased and pressures of 250 mm. the positive visual glow is the same as before. The positive starting potential is in general higher than for the negative abrased and also positive polished surfaces. The 350 SYLVAN J. CROOKER. ["SECOND [SERIES. negative glow voltage causes very faint " spears " or small brushes of light to flash out from sharp points here and there on the rough surface. These spears increase in size and number with increased potential, some being much brighter than others. As the potential is increased these spears unite into definite, clear beads which at times may be very steady and at other times may have more or less violent lateral movements. The negative starting voltage for abraised surfaces is much smaller than for the polished surfaces. At atmospheric pressures the positive glow on the abrased wire surfaces usually begins with a few small flashing purple streamers or brushes extending from the wire almost to the tube. These streamers are similar in appearance to the positive fans and streamers emitted from the surface of the enamel covered wire, see Figs. 3 and 4. These streamers increase in brightness and are accompanied by soft glow as the potential is in- creased. After a certain increase has taken place in the voltage these streamers disappear only the uniform glow remaining and increasing in brightness. For the abrased negative wire at atmospheric pressure the corona starts SURFACE CONDITION AND DIFFERENT SIZES OF WIRE No. 32 Cop No. 26 Coppe Pressures 7 No. 20 Cop>er P=Pollhe( A=Abralsec 6 7 KILO">'OLTS Fig. 5. with small flashing spears the same as for the abrased wire at 250 mm. These spears increase in number very rapidly with an increase in voltage, some of them collecting, so to speak, into small bright beads and then breaking up again. As the potential is still more increased the beads ] DIRECT CURRENT CORONA. 35 1 become more steady and definite, so that at times the abrased wire may be covered with many small, bright, steady and evenly spaced beads. Chemically Corroded Surfaces. The positive visual corona for corroded surfaces is essentially the same for all pressures as has been described for the abrased surfaces. At low pressures it begins with a faint flashing glow which becomes steady and uniform, increasing in brightness. At pressures of 250 mm. the appearance is the same as above, and for at- mospheric pressure the corona may start with the small purple brushes or fans and an accompanying glow, the fans soon disappearing and the glow becoming uniform and increasing in brightness. The positive glow generally begins at lower voltages for the corroded surfaces than for the polished. The negative visual corona for the corroded surfaces is likewise similar to that for abrased surfaces at the different pressures. Clear cut and steady beads are obtained at the lower pressures but are not as stable for the higher pressures. In general the negative starting voltage is lower than for polished surfaces. III. CHARACTERISTIC CURVES FOR DIFFERENT WIRES AND SURFACES. Varying the Radius of the Wire. The curves in Fig. 5 are taken for different sizes of copper wire. They show that the effect of abrasion in general lowers the starting point for copper wires at atmospheric pressure. The negative abrased curves are widely displaced from the polished ones, showing that more current flows in the corona discharge for the same voltage for wire abrased than for the smooth wire. The positive abrased curves quickly cross the polished ones and then continue to rise slightly displaced, less current flowing for the same potential abrased than for polished. Thus the abrased surface has the effect of restraining the flow of the positive current. The effect of abrasion is much greater in the case of the negative current. The curves also show that this effect is greater for the larger sizes of wire, which might be expected. The higher starting potentials for the larger-sized wires is also evident. The negative current builds up very slowly at first on the polished surface but finally reaches a point where it builds up much faster than the positive; at this point the beads are formed. The starting voltage for the abrased surface negative is much lower than for polished negative. The characteristic curve of the abrased wire is a smooth rising one eventually crossing the polished negative curve for large current values. This same phenomenon has been observed for different metals. Different Surface Conditions for the Same Metal. Fig. 6 gives the char- 352 SYLVAN J. CROOKER. [SECOND [SERIES. acteristic positive and negative curves for aluminum wires at about 50 mm., showing the effect of the three surface conditions; namely, polished, abrased and corroded. The starting positive wire voltage for the smooth surface is slightly lower than that of the negative, but the curves cross low, the positive current building up quite slowly with in- creased potential, while the negative curve is almost a straight line rising DIFFERENT SURFACES FOR ALUMINUM WIRE Diame.ter = 0.46 ram. Fig. 6. very rapidly. The positive starting potential is higher for the abrased surface than for the polished, while that for the negative abrased surface is lower. The negative polished and abrased surface curves cross but the positive do not. For the corroded surface the positive glow voltage is about the same as for the polished surface, the curve for the former con- dition becoming displaced shortly, less current flowing for the same voltage. The negative starting potential is very much lower in the latter case than that for the polished surface, bu t crosses at a low current value and rises to the right, less current flowing for the same potential. Thus it is seen that the surface condition has a very marked effect on the starting point of the corona as well as on the characteristic curves. All the wires were about 0.41 mm. in diameter. In general the abrased surface has the effect of lowering the starting potential for negative wire and raising it for positive wire. The starting point for both positive and negative in the case of corroded wires is in general lower than for the polished surfaces, but the corroded surface characteristics behave in VOL. VIII/I No. 4. DIRECT CURRENT CORONA. 353 rather an erratic manner, sometimes being displaced in one way and some- times in the opposite. Table II. gives a comparison between the corroded and polished wire characteristics for both positive and negative at different pressures. TABLE II. COMPARING CORRODED WITH POLISHED WIRE CHARACTERISTICS. Copper. Wire. Press. Starting Pot. Corroded Surface Characteristic. 50.2 Lower Raised. + 50.4 ii 250.0 < Crosses high. + 250.8 Raised. Steel. _ 53.2 Higher (press, diff.) Corsses high. + 52.4 Lower a ii 252.0 ii 11 low. + 252.4 ii Lowered. 739.4 ii Crosses high. + 739.4 ii " low. Aluminum. _ 51.9 Lower Crosses low. (For instance see Fig. 4.) + 51.9 ii . (5) Hence, when r = 7?i + 2. Calculation of the volume density of electrification in the space between the two concentric cylinders. For a system where the potential at a point is due to moving charges as well as static charges, we have Poisson's equation expressing the density in terms of the potential, V 2 F = - 47rp, (6) or, writing it in cylindrical coordinates, d 2 V i dV i d 2 F d*V VOL. X.I No. 3. J DISTRIBUTION OF POTENTIAL IN A CORONA TUBE. 273 For this particular case, the derivatives in z and < are zero, so rewriting the above equation, using total derivatives, d?V idV dr + r dr = 47T/7. (8) Since the density is an undetermined function of the radius, the equa- tion cannot be integrated directly. If, however, we plot the potential against the distance from the axis, a graphical method will aid in the determination of the density. That is, if the first derivative of the potential is determined from the curve for a series of values of r, these new values may be plotted against the radius again. By repeating this process with the derived curve, a relation between the second space derivative and the radius is obtained. From these two derived curves, then, the density may be computed according to equation (8). Fig. ii is a repetition of Curve 4, Fig. I, and Fig. 12 shows the density as computed for the different values of r. The density curve shows what we have deduced intuitively in regard I Fig. 11. Fig. 12. to the charges necessary to produce the observed distortion of the field. The large resultant negative charge near the positive wire and the positive charge near the negative tube should be expected. A peculiar maximum appears at about 2.7 cm. from the wire (Fig. 12). 4. Sources of Error. i. Potential assumed by a sphere in an ionized gas. It is difficult to draw conclusions as to the absolute potential of a sphere in a conducting gas, since it is very likely that the potential at an undis- turbed point in a gas is not the same as the potential assumed by a sphere when its center is at this point. In the case of a sphere near the positive electrode, its potential being initially the same as that of the gas, two streams of ions move in opposite directions past the side of the sphere, one containing a large number of 274 HARRY T. BOOTH. negative ions, and the other a smaller number of positive ions. It intercepts more negative ions than positive, so that its potential falls below that of the surrounding gas. The charge thus acquired by the sphere increases until the effect which it produces in attracting positive and repelling negative ions causes them to come in contact with the sphere in equal numbers. The final value of the potential assumed by the sphere is too high by an amount which depends upon the relative velocities of the positive and negative ions. Conversely, when the exploring sphere is close to the negative electrode, there are a greater number of positive ions intercepted than negative ions, so that the potential of the sphere rises above the potential of the undis- turbed gas, until finally an equilibrium is reached, the number of positive charges acquired by the sphere being equal to the number of negative charges. Thus the potential assumed by the sphere is greater than that of the undisturbed gas. If, however, the velocity of the positive ions is approximately equal to that of the negative ions, then the exploring point should attain very nearly the same potential as that of the surrounding gas. For the pressures used in this series of experiments, the velocities of the ions are nearly the same. Thus the error introduced could not have been very great. A slight error might be introduced if there was an appreciable voltmeter leakage between the point and the-power line. The shape of the point also affects the shape of the potential curve to a small degree. The volt- meters used were practically free from leakage, and the work was done during cold, dry weather, so the error introduced from this cause is neg- ligible. An attempt is being made to formulate the mathematical theory of the corona discharge, and it is hoped that these potential curves will aid in the solution of the problem. Summary. The distribution of potential between the electrodes of a corona tube was determined for four sizes of wire, for various pressures and potential differences. From these curves the density of the charge along the radius was derived by means of graphical methods. In conclusion, I wish to express my appreciation of the suggestions and advice given by Dr. Jakob Kunz, of this laboratory, and to Mr. J. W. Davis and Mr. R. W. Owens for the use of portions of their data on this problem. PHYSICS LABORATORY, UNIVERSITY OF ILLINOIS, May n, 1917. [Reprinted from the PHYSICAL REVIEW, N.S., Vol. X, No. 5, November, 1917.] THE PRESSURE INCREASE IN THE CORONA. BY EARLE H. WARNER. I. INTRODUCTION. IT has been reported by Farwell and Kunz that at the instant the corona appears about an axial wire in a cylindrical tube, the pressure of the gas in the tube suddenly increases. 1 It has always been stated that this pressure increase could not be due to heat, because of the in- stantaneous character of its appearance, and because of the rapidity with which it disappears as soon as the potential is removed from the wire. Since the only theories which have been advanced to explain the corona assume it to be an ionization phenomenon, it seemed reason- able to suppose that this pressure increase was due to the increase in the number of gas particles in the tube, and so it was called ionization pres- sure. Experiments have been performed and reported 2 which show that this pressure increase is exactly proportional to the corona current, with the wire positive when dry air, hydrogen, nitrogen, carbon dioxide, oxygen and ammonia are the gases in the tube. Since the publication of this data Arnold 3 has contended that the pressure increase could be completely accounted for as the result of Joule's heat, and that the assumption that it is due to ionization is untenable. To support this contention Arnold performed experiments " by electrically heating the central wire in apparatus similar to Farwell's and " observed the pressure increase. With such an apparatus Arnold attempted to show (i) that an increase in pressure due to heat appears suddenly, (2) that for a given power consumed in the tube the increase in pressure due to heat is of about " the same magnitude as those observed " in the corona. In order to show clearly that the pressure increase is not due to heat a series of comparative experiments were performed with the pressure increase caused, first, by producing the corona glow on the wire and, second, by heating the central wire. The pressure increase observed in the first set of experiments will be referred to as caused by corona and in the second set as caused by heat. 1 Dr. S. P. Farwell, "The Corona Produced by Continuous Potentials," Proc. A. I. E E. Nov., 1914. Dr. Jakob Kunz, "On the Initial Condition of the Corona Discharge," PHYS. REV., July, 1916. 2 Earle H. Warner, " Deterjnination of the Laws Relating Ionization Pressure to the Current in the Corona of Constant Potentials," PHYS. REV., Sept., 1916. H. D. Arnold, (Abstract) PHYS. REV., Jan., 1917. 484 EARLE H. WARNER. [SECOND [SERIES. Pressure Increase Due To Heat. 1.75 A few computations have also been made which strengthen the results of the experiments. II. EXPERIMENTAL RESULTS. 1. The reason why one who sees this pressure increase, as recorded by a quick-acting pressure meter, thinks it is not a heat effect, is because of rapidity with which it appears and disappears. Arnold showed that the pressure increase occurred quite rapidly when caused by heat. The following curves show the difference in the rapidity of appearance and disappearance of the pressure increase caused by heat, and caused by corona. It will be noticed in Fig. I, where the pressure increase was caused by heating the central wire, that fifteen seconds was required for the prssure to come to its maximum value, and that from the time the current was broken twenty-five seconds was required for the pressure to return to practically its original value, while in Fig. 2, where the pressure increase was caused by co- rona, only three seconds was required for the maximum pressure to be at- tained and that the pressure came back to practically its original value in eigh- teen seconds. In this last case from the appearance of the phenomenon it seems, if the aneroid pressure me- ter had less inertia, that the pressure increase could be determined in less than three seconds. These curves show that the pressure increase appears five times as rapidly when caused by corona as when caused by heat, and disap- pears also more rapidly. 2. In the pressure increase due to corona, a short time interval of five to seven seconds occurs after the sudden increase of pressure, before the heat effect in the corona begins to be noticed. This is shown by an abrupt bend, A, in the curve where the pressure in- crease is plotted against time, as is done in Fig. 3. No such bend occurs in the case where the pressure increase is caused by heat alone, as is shown in Fig. i . In the work which has previously been reported the pressure increase measurements were always taken at the point A , and this seems to be practically independent of the heat effect. 20 30 4o 50 Time in Seconds. Fig. 1. Pressure Increase Due To Corona. Fig. 2. VOL. X.I No. 5- J THE PRESSURE INCREASE IN THE CORONA. 485 3. The heat which is produced in the corona discharge, shown by the gradual pressure increase from B to C, Fig. 3, is distributed throughout the whole volume of enclosed air and so, when the current is broken does not radiate rapidly because the air is a poor conductor. This is shown very clearly in Fig. 4. This seems to show that the pressure increase due to Pressure Increase Due To Corona. 1.75 2.00 1.75 !.75 0.25 &' Pressure Increase Due To Corona. 10 20 30 40 50 60 70 Time in Seconds. 20 40 60 60 100 120 140 160 ISO 200 Time in Seconds. Fig. 3. Fig. 4. heat in the corona is represented by the difference of ordinates of C and B (Fig. 4). As soon as the corona current is broken at C the increase in pressure due to corona at once disappears, but the increase in pressure due to heat in the corona discharge remains, as is shown by the difference of ordinates of D and A . This difference is always very nearly equal to the difference of ordinates of C and B. This heat energy produced by the corona current, since it is distributed through the gas, radiates very slowly, as is shown by the gradual descent of the curve from D to E. No such effect is observed when the increase of pressure is due entirely to heat, as is shown in Fig. i. This curve (Fig. i) shows that twenty-five seconds after the current through the wire is broken at C the resultant pressure increase due to heat has practically disappeared; while Fig. 4 shows that twenty-five seconds after the corona is removed from the wire the increase in pressure due to the corona has disappeared, but practically all the pressure increase due to heat in the corona (ordinates C minus B approximately equals ordinates D minus A] still remains and radiates very slowly. 4. If the increase in pressure is due to heat, the same increase in pressure should result when the same power is consumed (a) with a corona current through the gas, (b) with a heating current through the wire. Figs. 5 and 6 show that this is not the case. The powers con- sumed in the two cases are not exactly the same, but one can see that were they the same, the increase in pressure due to corona would be approxi- 486 EARLE H. WARNER. [SECOND [SERIES. mately one half the increase in pressure due to heat. The power in the case of the corona was obtained by multiplying the potential difference between the wire and the tube by the corona current, and in the case of 1 nn 0.75 7 H 0.50 / r | m | 0.25 p ~epsu Due. 0.5 -e In To H >3S W ;reae< sat. itts ' NU-4- 10 20 30 40 50 60 70 Time in Seconds. Fig. 5. Fig. 6. the heated wire was obtained by multiplying the current through the wire by the potential difference across that portion of the wire which was in the tube. 5. If the increase in pressure in the corona discharge is due to heat the temperature of the air in the corona tube must increase. This may or may not be the case in the luminous layer near the wire but the tem- perature of the gas in the tube at a point four millimeters from the wire actually decreases. This was determined by inserting a sensitive ther- mocouple made of very fine Copper-Advance wire into the corona tube. The temperature decreased only at the instant the corona appeared. In a short time, after the heat due to the corona began to appear (corre- sponding to the slope B to C, Figs. 3 and 4) the temperature of the gas in the tube began to increase. This cooling effect is shown in Fig. 7. Comparing Figs. 7 and 3 it is seen that the increase in pressure which was measured at A was observed while there was an actual cooling in the corona tube. This cooling should be expected when air or oxygen are in the tube, for under these condi- tions ozone is formed. Since the formation of ozone from oxygen is always accompanied with an absorption of heat the temperature of the air or oxygen would tend to lower. Mr. J. W. Davis, working on corona about hot wires in hydrogen, has discovered that the appearance of the corona about a tungsten wire heated to white heat, causes it to cool to dull red. This tends to show that even in the corona glow itself there is a cooling effect. 6. If the increase in pressure in the corona is due to heat one should expect it to be the same with the wire either positive or negative. As has been previously mentioned it is impossible to obtain measurements it *J;H Cooling Effect in Corona, Ei lo 37 4J , Tim 1 & in Sec. 20 1 3 / Decrease Lr Galvanome VJ V* V Vfl ( ( / X^l ^^ Fig. 7. THE PRESSURE INCREASE IN THE CORONA. 487 when the wire is negative because of the presence of beads. The negative corona is entirely different from the positive corona. 7. The following consideration will further show that the increase in pressure can not be due to heat. The heat produced by the corona current will be given by the equation H = 0.238 eit and, if the observed pressure increase is due to heat, the increase in pressure Lp will be pro- portional to the heat, and we can write A = k eit. Now the only way for A to vary directly as i, the corona current, as is the case shown by curves in the last article is for e to be independent of i. Data shows that this is not the case. III. RESULTS FROM THEORETICAL CONSIDERATIONS. 1. If the increase in pressure is due to heat it is possible to compute the magnitude of the pressure increase when one knows the watts of electrical energy consumed in the tube. The trial represented in Fig. 6 gives us this data. The observed pressure increase was measured in three seconds so that the total number of joules of work consumed by the tube in that time was 3 X 0.266 = 0.798 joules and this corresponds to 0.1909 calories. Knowing the volume of the tube, the temperature and pressure of the air in it, the mass of the air in the tube can be com- puted. With the above-mentioned quantity of heat and mass of air, together with the specific heat of the air at constant volume, the temper- ature rise of the air can be computed, assuming that the electrical energy is converted into heat. This temperature rise comes out to be 2.44 C., which at constant volume corresponds to a pressure increase of about nine cm. of water, while the observed pressure increase in this particular trial amounts to about seven tenths cm. of water. In this computation radiation and conduction losses have been neglected because they would be very small from a body 2.44 C. above room temperature. This shows that the observed results lie in a different order of magnitude from what would be expected if Arnold's theory were true. 2. Arnold states, if "we compute the corona currents that would result from the presence of enough ionized particles to produce the ob- served pressure changes, the currents calculated are many thousand times greater than those actually obtained." Such a statement is only true when the ionized particles are produced in a uniform or practically uni- form electric field. This is not the case in the corona tube. H. T. Booth is publishing data on the distortion of the field in the corona tube. This data shows that the potential gradient near the wire is very high of the order of 30,000 volts per cm. This is the arcing gradient, in which it is probable every molecule is ionized. Then for a long space between the 4 88 EARLE H. WARNER. [SECOND [SERIES, 0.600 1400 Current As a Function of Pressure / Constant Voltage | / Hydrogen. / *4 wire and the tube there is a very small gradient. With this condition of the field, near the wire every molecule may be ionized and still the resultant current be very small, for few of the ionized particles near the wire will pass through the space where there is a small gradient. Simple I8on _ computations based on kinetic theory show that the maximum observed pressure increases can be explained by ionization if every molecule of the air with- in 1.39 mm. of the wire is ionized. Within this distance the potential gradient is equal to the arcing gradient and therefore probable that all mole- cules are ionized. IV. FURTHER VERIFICATION OF KUNZ'S THEORY. The final equation as pre- sented in the last article is ki = (pi po) + a constant, 6 where i is the corona current, VQ the volume of the tube, e the potential difference between the wire and the tube, pi po the pressure increase, k a con- stant and po the initial pressure. This equation shows that for a con- stant potential difference e, the current i should increase as po is low- ered. Data were taken, by measuring the current at various measured pressures, caused by a constant potential difference, which verifies this theory. These data are shown graphically in Figs. 8 and 9 when pure hydrogen and nitrogen respectively were the gases in the tube. Fig. 8. V. SUMMARY AND CONCLUSIONS. Experimental results show: 1. That the increase in pressure due to corona appears and disappears much more rapidly than when due simply to heat. 2. That the heat in the corona discharge is not a prominent factor until many seconds after the corona appears. VOL. X.l No. s- J THE PRESSURE INCREASE IN THE CORONA. 3. That in equal energy experiments the increase in pressure due to corona differs from the increase in pressure due to heat by about 50 per cent. 4. That at the instant the corona appears the gas in the tube at a small distance from the wire is cooled. 600 200 Current As a function of Pressure. Constant Voltage Hitrogen Wire + 7620 77 720 680 640 600 Pressure in Mm. of Mercury. 560 520 Fig. 9. 5. That the theory advanced by Kunz is verified in one more field, namely in the relation between current and pressure for constant voltage. These results together with conclusions drawn from simple calculations, force one to believe that the pressure increase in the corona discharge is not due to Joule's heat. With the recent knowledge of the distortion of the field in the corona tube it seems very possible that the increase in pressure is due to ionization. The writer desires to express his appreciation to Professor A. P. Carman for the use of the laboratory facilities, and to Dr. Jakob Kunz for his continued interest and suggestions. LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS, June, 1917. Reprinted troin the PHYSICAL REVIEW. N.a.. Vol. XII, No i. July, 1918.] ON BOHR'S ATOM AND MAGNETISM. BY JAKOB KUNZ. pHERE are two outstanding problems in the field of physics at the present time, the problem of the nature of light and its origin and the problem of magnetism. Light and magnetism seem to be very directly connected with electrical charges in motion and the ultimate theory of the origin of light may involve the solution of the problem of magnetism. Several attempts have been made at an explanation of the radiation of the black body and of the emission of line spectra. The most surprising fact that has been brought to light by these investiga- tions is the existence of the quantum constant h, which seems to belong to the fundamental constants of nature. Among the various attempts at an explanation of the series spectra, the theory of the atom by Bohr deserves special attention because it involves h and accounts with very surprising accuracy for the Rydberg constant of the Balmer and related series. According to Bohr the atom consists of a nucleus surrounded by electrons revolving in stationary non-radiating orbits, for which the laws of electrostatics hold so that we have : ee\ mv 2 ~a? = '' ~a ' The stationary circles are determined by the postulate that the kinetic energy y<#mP is proportional to the quantum of energy such that (z = integer) mv2irna = zhn mva 27T hence the constant h is proportional to the moment of momentum of the revolving electron. It is also proportional to the magnetic moment M of the electron in the stationary orbit, thus e M = Tra 2 i = 7ra 2 en = zh - . 47TW The non-radiating orbit of the electron seems to account at once for the constant magnetic properties of the elements and their compounds. 60 JAKOB KUNZ. When the electron moves from an outer to an inner stationary orbit, it loses a quantum of energy, giving rise to a line in the spectrum ; 27r 2 me 2 ei 2 Two of the fundamental problems seem to be solved at the same time, the electron, when jumping from an outer to an inner stationary orbit giving rise to light and when moving undisturbed in a stationary orbit, producing the magnetic effects. Of course even if both parts of the theory were verified, the question would still remain, why such non- radiating orbits are possible, in other words, why Maxwell's theory of electromagnetic radiation does not hold within the atom. If this theory is invalid within the atom, then we might expect also that the theory of relativity does not hold in the same regions. Before I proceed to the discussion of magnetism on the basis of Bohr's theory, I wish to call attention to an interesting conclusion with regard to the velocities of those electrons near the nucleus which give rise to the Roentgen spectra, the approximate law of which has been discovered by Moseley. The square root of the highest frqeuencies from the atoms of the chemical elements is proportional to the charge e\ of the nucleus. This law follows from Bohr's theory. If we call the nuclear charges of two atoms e n and e 12 and assume the factor i/z 2 i/zi 2 to be the same in both elements, then we obtain from equation (i) for the highest fre- quencies of the two elements n\ where NI and 7V 2 are the corresponding atomic numbers. Now, Millikan has tested this relation for tungsten and hydrogen and has concluded that the shortest wave-length which could be produced by hydrogen is 91.4, while Lyman found for the convergence wave-length 91.2/4/4. This would correspond to the highest frequency of the hydrogen atom. It seems certain that the Lyman ultra-violet series of hydrogen lines is the K series of this element. While this agreement is very satisfactory, it should be remarked that we have as yet no proof of the existence of Balmer series in the Roentgen spectra, and the resolving power of the crystals for the characteristic Roentgen rays may be too small, so that it remains impossible with the present experimental means to discover series analogous to Balmer series in the Roentgen spectra. Now the relation 1^1 = e JL > H 6 62 N 2 VoL.^XII.J QN BOHR >s ATOM AND MAGNETISM. 6 1 may be true, even if Bohr's theory of the atom is not true, provided we introduce the quantum relation in the following way, as has been shown by F. Sanford. 1 s* r 1) y&wv 2 = hn v = 2irna = \l \n \ ^Yt mva = h/ir 2) mv 2 /a = eei/ a 2 e\ = mv 2 a/e = = vh/ire ire 62. n z Whether we deduce this relation according to Sanford 's or to Bohr's method- we assume in both cases that the mass m of the electron is the same in both and in all elements. In the theory of relativity the ratio of the transversal mass m of the moving electron to the mass m^ of the electron at rest is given by m i m Q i - v 2 If we assume i.oi for w/w we find v = 4.2 -io 9 cm. per sec. If the shortest wave-length X measured for tungsten is equal to o.i67-io~ 8 cm. then n =^- = i.8-io 1& A but eei mv 2 = - - a 2 a 2 i 2 i 2 4 From (4) l = Oj e z ~ ai 1 PHYSICAL REVIEW, Vol. IX., p. 383, 1917. 62 JAKOB KUNZ. [slms. for two different elements. For the hydrogen atom 0i = 5-5-io- 9 cm. for tungsten Ni Ji N 2 74' hence a 2 = 743'io~ n cm. for the innermost orbit of the electron in the tungsten atom, and the circular velocity v 2 = 2irna 2 = 8.38 -io+ 9 cm. For the uranium atom we would find a path velocity of the electron in the innermost orbit amounting to 2.I-IO 10 cm., approaching somewhat the velocity of light. This velocity would correspond to a mass m = 1.4^0, if we neglect the influence of other revolving electrons. It is remarkable that these highest velocities of revolving electrons remain only about 30 per cent, below the velocity of light, on the other hand a satisfactory theory of the Roentgen spectra must take this effect into account or deny relativity in the interior of the atom. The velocity of the electrons in the orbits of Bohr's atom is so great, that it seems possible to explain the magnetic properties of the elements by the assumption of a few electrons revolving in nonradiating orbits. We shall proceed to compare the magnetic properties of some of the sim- plest elements with Bohr's theory of the atoms and molecules. The first difficulty which we encounter consists in the fact that we have measured so far only the magnetic properties of molecules (except the rare gases) and not of atoms and that Bohr's theory of the molecules, of hydrogen for instance, is not so definite as that of the atoms. The hydrogen atom consists of a nucleus of charge e\ and an electron of charge e, revolving in a circular orbit around about the nucleus. This atom represents an elementary magnet and if the hydrogen gas were made up of atoms it would be paramagnetic and the paramagnetic sus- ceptibility could be evaluated at once. But now the question arises as to the nature of the coupling of two atoms in a molecule. The ele- mentary magnets of two atoms may arrange themselves so that the axes of the two magnetons form the same line, hydrogen would then still be paramagnetic, or the axes may be parallel to each other and the neigh- boring poles be of opposite sign, the hydrogen gas would then be dia- No^'i* 11 '] ON BOHR'S ATOM AND MAGNETISM. 63 magnetic; finally, and this is the case Bohr has assumed for the hydrogen molecule, both electrons revolve in the same orbit, separated by 180, the plane of the orbit being at right angles to the line joining the two nuclei. Bohr calculates for the radius of the common orbit of the electrons a = 5.22-io~ 9 cm., for the frequency n = 6.72 -io 15 . This gas is paramagnetic. The magnetic moment M is equal to : M = 2-jra 2 en = 1.82-iQ- 20 The magnetic susceptibility at o NM 2 _ 2.72-io 19 (i.82) 2 -io- 40 ~3*T = 3-1, 37" io 16 - 273 k = + 8.2 io~ 8 per unit volume at o. The values which I find in the literature are contradictory: + o.8-io~ 8 (Quincke), o.5-io~ 8 (Bernstein), o.34-io~ 8 (Blondlot). A further accurate determination of the magnetic properties of hydrogen is very necessary. The helium atom in Bohr's theory consists of a nucleus of charge 2e around which there are rotating 2 electrons in the same orbit of radius a = o.3i4'io~ 8 cm., with a frequency n = 19. io 15 . This gas would be paramagnetic. The magnetic moment of the atom is equal to 1 .85 io~ 20 , the susceptibility k = 8.5 -io~ 8 at o; for both gases k = C/T where Curie's constant C = NM 2 /^R. Helium like the other inert gases is diamagnetic. Here Bohr's theory is in contradiction with the experi- mental fact. Lithium is supposed to contain a nucleus of charge 30; two electrons revolve in the inner orbit and one electron in the outer orbit in the same direction, giving rise to paramagnetism ; the magnetic moment can easily be calculated. M = 2ira 1 2 en 1 + ira 2 2 en 2 = 2.815- icr 20 , 01 = i.99-io~ 9 a 2 = 0.651 -icr 8 , HI = 4.74 -io 16 n 2 = 443 -io 15 . The paramagnetic susceptibility of lithium would be equal to: NM 2 2.72 io 19 (2.8i5) 2 io- 40 3 -i. 37 -io- 16 273 . . k = ~^ = - = + I.Q8-IQ- 7 - 16 per unit volume at o. Lithium like the other alkali metals is weakly paramagnetic. The literature contains the value 2.26- io~ 7 , which agrees 64 JAKOB KUNZ. [!ER?ES D with the theoretical value even better than we should expect, because we have treated lithium like a gas, while for the solid state the mutual action of the elementary magnets must be taken into account. Finally, beryllium, in Bohr's theory, consists of a nuclear charge 40 with two orbits, each containing two electrons. If the radii and the frequencies of the electrons in the neutral state of the atom were uniquely determined, the magnetic moment and the magnetic susceptibility could easily be calculated. The atom model is paramagnetic in agreement with experimental determinations. All four substances, hydrogen, helium, lithium, beryllium, are para- magnetic according to Bohr's theory, while hydrogen is probably dia- magnetic and helium is almost certainly diamagnetic. The effect of a magnetic field on a paramagnetic gas consists in the orientation of the molecular magnets into the direction of the external field; so that there will be a state of equilibrium between the directing tendency of the field and the disturbing tendency of the temperature agitation. As far as this effect of the field is concerned, we are justified in applying the theory of paramagnetism to Bohr's atom model. But the field must also have a secondary effect on paramagnetism, an effect which determines at the same time the diamagnetic properties. Let us consider in a diamagnetic gas an atom with an electronic orbit of radius a, the electron e revolving with velocity v in a plane perpen- dicular to the magnetic field. The magnetic moment, without the action of the external field, will be equal to M = Tra 2 en- if a field H is applied the frequency will change so that dM = 7re(2anda + a 2 dn) or assuming the first term small, jnp dM = irea 2 dn = irea 2 . But in the theory of diamagnetism as well as in Lorentz's theory of the simple Zeeman effect, it is assumed that mv 2 - that is, the centripetal force, which balances the centrifugal force is pro- portional to the distance a between the electron and the center of the atom, the centripetal force is a quasi elastic force; while in Bohr's theory the centripetal force is inversely proportional to the square of the dis- tance between the electron and the nucleus. Yet even under these circumstances we can find, allowing certain approximations, the older No^"i XIL ] ON BOHR'S ATOM AND MAGNETISM. 65 expressions for the diamagnetic susceptibility and for the Zeeman effect, except for a factor 2, as will be seen from the following deductions which are self explanatory. mv 2 f a a? With a magnetic field we have : mv 2 f mv 2 a = - 2 - Hev = -7,- - Hev mv 2 mv 2 a Hev a' 2 a' 3 a' 2ira 2ira' = j^ = ~, = Constant, He 2irm \ -^72 i^> ; I = -=f , He 2irm ' a /s _He but a' = a + da, a' 3 = a 3 + $a 2 da T r = T + dT, T' 2 = T 2 - hence He - T , i da =^dT = (2Tra/2wT)dT = ^dT t He " 3 * = ~ He ' dr He = an = -- - = HI n t jf 2 2irm He = n HZ, He 66 JAKOB KUNZ. which is the formula for the Zeeman effect except for the factor J^. This explanation of the Zeeman effect is open to a logical objection; namely, in Bohr's theory it is assumed that a line of the spectrum is emitted when an electron moves, we do not know on which path, from an outer to an inner non-radiating orbit. The magnetic field, of course, acts on the electron during the emission of light; that is, while the electron moves from one orbit to the other. But in this present theory, as in the older Lorentz theory, we assume that the magnetic field affects only the stationary orbits. This assumption however remains valid for the determination of the diamagnetic susceptibility which we shall now consider. 2 dM- -*'^- = --. If there are N orbits per unit volume and if the axes are uniformly distributed in all directions, then we have eWNH M = ,- , 6M or, the diamagnetic susceptibility k is equal to k = 6m ' or, twice as large as the same quantity calculated on Lorentz's assumption that the centripetal forces are proportional to the distance between the electron and the center of the atom. For the diamagnetic suscepti- bility and for the Zeeman effect we have to assume in Bohr's atom that under the influence of the magnetic field the nonradiating orbits are slightly changed. For a paramagnetic gas the resultant susceptibility would be the difference 3#r " 6m ' For hydrogen we would have 4.7r 2 a*eVN e 2 a?N2 k = If we take again for o c ON BOHR'S ATOM AND MAGNETISM. a = 5.22 -lo- 9 , n = 6.72-I0 15 , m = 9.01 -lO" 28 , R = I.37-IO- 16 , T = 273. We find: = 3-7 -io 26 , that shows that the paramagnetic effect for hydrogen at o is more than i ,000 times larger than the diamagnetic effect. For helium we have the corrected paramagnetic susceptibility equal to : N a M* K 6m M 2ira?en, With the previously given values for the radius a and the frequency n of the electrons we find 222 = I.26-I0 30 . The relative diamagnetic effect of helium is a little smaller than the corresponding effect of hydrogen. In general, the observed susceptibility k is the difference between the paramagnetic susceptibility k p and the diamagnetic susceptibility k a k = k p kd. It is therefore quite conceivable that an element like tin changes at given temperatures from the negative to the positive sign of magnetism, and vice versa; k p at all events is a function of temperature. For the diamagnetic gases the susceptibility is probably almost independent of temperature. If Bohr's theory of the structure of helium is in the right direction toward the physical reality then we have to make a little modification in order to explain the magnetic properties of helium. If the principle of conservation of the moment of momentum holds within 68 JAKOB KUNZ. \ the atom, if this momentum is proportional to the magnet moment and if the electrons are moving in elliptic orbits, then the nucleus would also move around the center of attraction of the system, in the same direction as the electrons, the magnetic moments of the electrons and the nucleus would balance each other and the atom would be diamagnetic. Of course, it is not required that the resultant moment should be exactly zero, but only that the absolute value of k d should be larger than k p . If over a wide range of temperature of a gas k were independent of the temperature then k p would be equal to zero. The Zeeman effect of iron vapor shows that the diamagnetic properties persist up to very high temperatures, and the additive law of diamagnetism for organic com- pounds of similar constitution indicates that the diamagnetism is a rather deep seated property of matter, which may be attributed partly to the nucleus. On the other hand the paramagnetic phenomena and the diamagnetic properties of solid and liquid substances are readily influenced by chemical and mechanical agencies. SUMMARY. i. It has been shown that the relation 1 can be deduced by means of the quantum relation without Bohr's theory of the atom. 2. If we calculate the radii of the orbits and the velocities v of the electrons near the nucleus of the atom by means of the relations : ei N! a 2 = di - = ai , e 2 N 2 V 2 = 2irna 2 , we find for the greatest velocity of the electrons in the uranium atom 2.I-IO 10 cm. corresponding to a mass m of the electron equal to i.4W . 3. The paramagnetic moments and the paramagnetic susceptibilities of hydrogen, helium and lithium have been calculated by means of Bohr's theory. If hydrogen really is diamagnetic, which has yet to be decided by experimental measurements, the magnetic properties of hydrogen and helium can not be explained by Bohr's atom-model. In this case a new model has to be invented, or the magnetic properties have to be ascribed to different causes, for instance, to proper magnetons, independent of revolving electrons, or to electrons whose charge itself is No L 'i XIL ] ON BOHR'S ATOM AND MAGNETISM. 69 in motion, so that the electron is at the same time a magneton or to the nucleus as being responsible partly for the magnetic phenomena. 4. A modification of the simple Zeeman effect has been given. The resultant equation He #2 n\ = 7TW differs from Lorentz's theory by the factor %. 5. The diamagnetic susceptibility of hydrogen and helium has been calculated. It is about 1,000 times smaller than the paramagnetic susceptibility. 6. A modification of Bohr's atom has been considered, which will account for the diamagnetic properties of He. LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS, April, 1918. THE MAGNETIC PROPERTIES OF SOME RARE EARTH OXIDES AS A FUNCTION OF THE TEMPERATURE. [Reprinted from the PHYSICAL REVIEW, N. S., Vol. XII, No. 2, August, 1918.] THE MAGNETIC PROPERTIES OF SOME RARE EARTH OXIDES AS A FUNCTION OF THE TEMPERATURE. BY E. H. WILLIAMS. THE existence or non-existence of the magneton, the elementary quantity of magnetism corresponding to the electron of elec- tricity, has attracted the attention of investigators since it was first suggested by Ritz. Much work has been done, especially by Weiss, Kammerling Onnes, du Bois, Honda, Perrier. Piccard and Terry, and while the preponderance of the results obtained by these investigators is against the elementary moment of magnetism as suggested by Weiss, yet the idea is still strongly maintained by some. Within the last three years Piccard 1 maintains that there is a group of bodies (paramagnetic) which obey strictly Curie's law and hence he argues that the foundations of the theory are sound and there is still evidence in favor of the magneton. Not. only was it hoped to get evidence for or against the magneton theory, but the opportunity to obtain from the Chemistry Department of the University of Illinois rare earths in a very pure state from which were being made atomic weight determinations made it desirable to investigate their magnetic constants. My thanks are due to Dr. Hopkins and his associates of the Chemistry Department for their hearty co- operation in supplying me with samples of the rare earth materials. The method used was that of Curie 2 which consists in measuring the pull exerted on an object placed in a non-uniform magnetic field. Accord- ing to this method X, the magnetic susceptibility per unit mass, is given by the expression OX providing the force is measured by means of the twist of a suspension. In this expression M is the mass of the sample, H v the field at right angles to the direction of motion of the sample, dH y /d x the variation of this field along- the direction of motion, C the couple necessary to twist the 1 Piccard, Arch, des Sci. Phys. et Nat., 40, 278, 1915. 2 P. Curie, Ann. de Chem. et de Phys., (7), 5, 298, 1895. VOL. XII. No. 2. MAGNETIC PROPERTIES OF RARE EARTH OXIDES. suspension through one radian, the angle of twist in radians and / the lever arm from the line of suspension to the sample. The torsion balance was contained in a wooden box put together without the use of any magnetic material. The suspension consisted of a phosphor-bronze wire the torsion couple of which was 940 dyne cm. at 25 C. It was found that this varied with the temperature, the variation being about 0.6 dyne cm. for i C. Since, in some cases, the box containing the torsion balance warmed up five or six degrees Centigrade, a correction was made for the variation of the torsion couple. During the first part of the work an aluminum rod was used for the lever arm and pointer of the balance but the zero corrections for this were so large that it was deemed advisable to find another system. The system finally adopted consisted of glass which was slightly diamagnetic counterpoised with a small amount of aluminum which was slightly paramagnetic. By using the right amount of aluminum the zero correc- tion could be made very small. Several sets of values of H y and dH y /dx were plotted and from the mean curve values were taken for the product H y (dH y /dx). These products were in turn plotted and the point in the field where the product was a maximum was determined. The apparatus was now set so that the center of the test coil was at the point in the field where the product H y (dH y /dx) was a maximum and the values of H y and dH y /dx determined for various currents in the electromagnet. The mean of four such sets is given in Table I. TABLE 'I. /. H. &HI&X. //(A/r/A^r.) 1.5 amp. 1020 205.4 209.5 X 10 3 2.0 1352 273.7 370.1 2.5 1687 338.5 571.1 3.0 2012 407.2 819.2 3.5 2351 473.0 1112.1 4.0 2659 530.7 1411.0 4.5 2968 596.4 1770.0 5.0 3267 648.9 2120.0 The couple C necessary to twist the suspension through unit angle was found by the ordinary vibration method. An accurately turned disc and ring were used for known moments of inertia and C calculated from the formula C--*^- (2) U ~~ ft'* __ A\ \ 2 ) i6o E. H. WILLIAMS. ["SECOND [SERIES. where 7 is the known moment of inertia added to change the period from t to t f . The oxides of seven of the rare earths, namely, erbium (Er 2 O 3 ), dysprosium (Dy 2 O 3 ), gadolinium (Gd 2 O 3 ), samarium (Sa 2 O 3 ), neodymium (Nd 2 O 3 ), lanthanum (La 2 O 3 ) and yttrium (Yt 2 O 3 ), were investigated. Before using any of the oxides, they were heated to a temperature of about 1000 C. in a platinum crucible in order to decompose any carbonate which may have formed and to drive off all moisture. The samples under investigation were contained in a silica capsule which was fitted to one arm of the torsion balance. The balance, with thermocouple and empty capsule in place, was first calibrated for fields due to currents of from 1.5 to 5 amperes and for temperatures from 25 C. to 300 C. Table II. gives a sample set of data for Gd 2 O 3 with the thermocouple "Mass of sample = .11912 gm. torsion balance = 105.7 cm. TABLE II. 99 + Per Cent. Pure. Lever arm of sample = 10.55 cm. Scale distance of Temp. Current in Magnet. Deflection of Torsion Balance. Corrected Deflec- tion. XX*. 21.8 C. 1.5 amp. 2.0 2.5 3.0 7.81 cm. 13.79 21.31 30.21 7.59 cm. 13.47 20.93 29.86 128.3 128.9 129.8 129.1 . Mean 129.0 103.2 11 1.5 2.0 2.5 3.0 3.5 6.12 11.11 16.80 23.74 31.82 5.98 10.93 16.64 23.61 31.75 101.1 104.6 103.2 102.1 101.1 Mean 102.4 178.0 1.5 2.0 2.5 3.0 3.5 5.16 9.13 14.15 20.03 26.63 5.07 9.04 14.10 20.03 26.73 85.5 86.3 87.2 86.4 84.9 Mean 86.1 269.5 ii 1.5 2.0 2.5 3.0 3.5 4.15 7.43 11.65 16.49 21.87 4.07 7.37 11.63 16.59 22.10 68.6 70.3 71.9 71.5 70.2 Mean 70.5 VOL. XII." No. 2. MAGNETIC PROPERTIES OF RARE EARTH OXIDES. 161 and torsion balance readings omitted. Four such sets of data were taken with different samples of the same material. One curve repre- senting the four sets of data was drawn in which magnetic susceptibility was plotted against temperature. From this curve values were taken to test Curie's law. In like manner the other oxides were tested and results plotted. From these curves the results in the first and third columns of Tables III., IV., V. and VI. were obtained. For each temperature the value of the magnetic susceptibility X, is the mean of the values obtained from four or five fields as in Table II. TABLE III. Gadolinium Oxide QQ + Per Cent. Pure. t. T. XX io 6 . XTX io. jrcr+i2)xio6. 20 293 130.1 38119 39680 60 333 115.1 38328 39709 120 393 98.2 38593 39771 180 453 85.5 38731 39757 240 513 75.6 38783 39690 300 573 67.8 38849 39663 TABLE IV. Erbium Oxide QQ.6 + Per Cent. Pure. t. T. A'X io<5. XTX io. *'( T+ 13.5) X io. 20 293 189.1 55406 57954 60 333 167.2 55678 57935 120 393 142.6 56042 57967 180 453 124.4 56354 58033 240 513 110.1 56462 57969 280 553 102.2 56516 57895 TABLE V. Dysprosium Oxide 09.5 + Per Cent. Pure. t. T. XX io<5. XTX 106. A'( T+ 15) X 106. 20 293 234.1 68591 72103 60 333 207.4 69064 72175 120 393 176.7 69443 72094 180 453 153.9 69717 72025 240 513 136.6 70076 72125 300 573 122.6 70250 72089 162 E. H. WILLIAMS. [SECOND [SERIES. TABLE VI. Neodymium Oxide 99.5+ Per Cent. Pure. t. T. A' X ioe. x A'7'X io 6 - j X( T+ 44) X io 6 . 23 296 29.3 8672.8 9962.0 103.4 376.4 23.7 8920.7 9963.5 179.4 452.4 19.8 8957.5 9828.7 283.0 556 16.6 9229.6 9960.0 TABLE VII. Samarium Oxide 99.5+ Per Cent. Pure. Temp. 22.3 101.8 270.2 6.02 5.93 5.98 Mean 5.98 TABLE VIII. Lanthanum Oxide 99 + Per Cent. Pure. Temp. Hy. Corrected Def. XX io. 24 C. 2025 -0.09 -0.49 n 2660 -0.13 -0.41 3010 -0.14 -0.36 3328 -0.16 -0.34 Mean -0.40 TABLE IX. Yttrium Oxide 99.5 + Per Cent. Pure. Temp. Hy. Corrected Def. A-Xo. 22 C. 2025 .09 .60 2351 .11 .52 a 2660 .13 .48 3010 .17 .51 3328 .21 .52 Mean .53 Samarium oxide, Table VII., shows no variation of magnetic suscepti- bility with temperature. Three sets of data similar to that in Table II. were taken, all of which are summarized in Table VII. In the case of lanthanum oxide and yttrium oxide, Tables VIII. and IX., the magnetic susceptibility was so small that no attempt was made to study the varia- tion of the susceptibility with the temperature. In the case of lanthanum oxide the magnetic susceptibility is negative, thus indicating that this oxide is diamagnetic whereas all the others are paramagnetic. No L ' 2 XIL ] MAGNETIC PROPERTIES OF RARE EARTH OXIDES. 163 According to Curie's law the susceptibility of paramagnetic bodies times the absolute temperature is equal to a constant; that is, XT = con- stant. An examination of Tables III., IV., V. and VI. shows that the law does not hold for any of the materials investigated. However, they are found to follow quite closely a modification of Curie's law, namely, the susceptibility times the absolute temperature plus a constant is equal to a constant, X(T + 0) = constant, in which each material has its own value of 6. TABLE X. Williams. Levy. Oxideof XXIQ6 X X io Yttrium ....................... 53 (22 C.) -.14 Lanthanum ................... -.40 (24 C.) -.18 Neodymium .................. 29.3 (23 C.) 33.5 Samarium .................... 5.98 6.5 Gadolinium ................... 130.1 (20 C.) 161. Dysprosium ................... 234.1 (20 C.) 290. Erbium ....................... 189.1 (20 C.) Table X. gives a summary of the results obtained together with results quoted by Levy in his book on "The Rare Earths," page 153, 1915. Various explanations have been advanced for the variation from Curie's law. Oosterhuis, 1 from a consideration of zero point energy, deduces an explanation as follows: Taking the value of the rotational energy of the molecule as deduced by Einstein and Stern 2 to be U = e hnikT _ ~ where h is Planck's constant and n the frequency of the rotation, and further assuming that this rotational energy is inversely proportional to the magnetic susceptibility X as developed by Langevin, 3 , Oosterhuis deduces the relation X(T + 6) = C, where 6 = \ ^~ . 6 R Since 47T 2 /' where / is the moment of inertia of the molecule, he concludes that mole- cules with a small moment of inertia will have a large value of 6, a large zero point energy (J/2/m ) and deviate markedly from Curie's law. 1 Phys. Zeit., 14, 862, 1913. 2 Ann. d. Phys., 40, 551, 1913. 3 Ann. Chem. Phys., (8), 5, 70, 1905. 164 E. H. WILLIAMS. [SECOND [SERIES. Although the results given above (Tables III., IV., V. and VI.) follow a modified form of Curie's law, 6 does not vary inversely as the moment of inertia of the molecule as is shown in Table XI. TABLE XI. Oxide. At. Wt. t. Molecular Wt. Molecular Wt. X0. Erbium 167.7 13.5 383.4 5176 Dysprosium 162.5 15. 373.0 5595 Gadolinium Neodymium 157.3 144.3 12. . 44. 362.6 336.6 4351 14810 Starting from an entirely different viewpoint Kunz 1 has derived the same expression for the variation of the magnetic susceptibility with the temperature. He points out that since it is quite likely that the electrons responsible for the paramagnetism revolve in the outer layer of the atom, the molecular moment will be the resultant of all the atomic moments of the atoms. Furthermore, with increasing temperature, it is quite likely that the atoms share the energy of temperature agitation which also will affect the resultant magnetic moment of the molecule. Therefore, in general, we may express the molecular moment as M = Mof(T). In solid or liquid paramagnetic substances the forces which oppose the tendency of the external field to direct the elementary magnets is composed of the temperature agitation R T together with a force due to the mutual effect of the molecules on each other and which would be a certain function of the temperature fi(T). With these assumptions Kunz obtains for particular values of f(T) and/i(7 1 ), X(T + 0) = constant. All of the substances included in this investigation which vary with the temperature obey the modified Curie law instead of the law itself. In the case of samarium oxide the magnetic susceptibility is found to be inde- pendent of the temperature. This is also probably true of lanthanum oxide and yttrium oxide. It may appear from Table II. that the magnetic susceptibility varies with the field strength thus indicating that the substance is ferromagnetic in nature but the remainder of the data does not bear out this conclusion. In some cases the magnetic susceptibility came out very nearly constant for the different field strengths, while in others it varied in the opposite way to which it appears to vary in Table II. A careful study of all the data leads one to conclude that all the oxides are paramagnetic. 1 PHYS. REV., VI., 2, 113, 1915. No L ' 2 XIL l MAGNETIC PROPERTIES OF RARE EARTH OXIDES. 165 It was thought worth while to test the accuracy of an analysis of rare earths by the magnetic method. To do this two pure substances were mixed in known proportions and the magnetic susceptibility of the mixture determined. The results, given in Tables XII. and XIII. , show very close agreement between the percentage by weight and the percentage by the measurement of the magnetic susceptibility. The magnetic method would not be adaptable if the mixture consisted of more than two substances. TABLE XII. Er 2 O 3 09095 gm. Yt 2 O 3 .06735 gnu Total 15830 gm. Per cent, of Er 2 O 3 by weight 57.45 per cent. Per Cent, by the Magnetic Method. Substance. A'X io. Er 2 O 3 (99.6 per cent, pure) 187.7 (at 22.3 C.) Yt 2 O 3 (99.6 per cent, pure) ' 53 Mixture 108.1 (at 22.3 C.) Per cent. Er 2 O 3 by the magnetic method 57.71 per cent. TABLE XIII. Per Cent, by Weight. Er 2 O 3 06985 gm. Sa 2 O 3 .06767 gnu Total 13752 gm. Per cent, of Er 2 O 3 by weight 50.79 per cent. Per Cent, by the Magnetic Method. Substance. A'X 106. Er 2 O 3 (99.6 per cent, pure) 187.9 (at 21.7 C.) Sa 2 O 3 (99.5 per cent, pure) 5.98 Mixture 98.9 (at 21.7 C.) Per cent, of Er 2 O by magnetic method 51.08 per cent. SUMMARY. The mass susceptibilities for the oxides of erbium, dysprosium, gado- linium, samarium, neodymium, lanthanum and yttrium have been meas- ured for temperatures from 25 C. to 300 C. and all found to be para- magnetic with the exception of lanthanum which was slightly dia- magnetic. In those cases where the susceptibility varies with the temperature Curie's law is not found to hold but the results follow quite closely a modification of this law, namely, X(T + 6) = constant. It follows that 1 66 E. H. WILLIAMS. [s in so far as Curie's law is essential to the existence or determination of the magneton the results obtained are unfavorable. The magnetic susceptibility does not vaYy with the field strength. The results are explainable either by the theory worked out by Kunz or the zero point energy theory of Oosterhuis. LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS, URBANA, ILLINOIS, February, 1918. [Reprinted from the PHYSICAL REVIEW, N.S., Voi XIII. No. 2, February, 1919. m- "awn vwwwv /wvwv\ il \MM/W WV\ Fig. 1. AMPLIFICATION OF THE PHOTOELECTRIC CURRENT BY MEAN3 OF THE AUDION. BY CARL ELI PIKE. A METHOD has been outlined by Jakob Kunz 1 by means of which the photoelectric current may be amplified, thus making the photo- electric cell more useful as a photometer, especially in the region of ultra- violet light and also for technical purposes. The amplification is produced by means of a vacuum tube with three electrodes, or the audion. In order to determine the best potentials to use in the primary and secondary circuits it is necessary to know the characteristic curves for the audions used. The characteristic curves of several audions have been deter- mined by an arrangement of apparatus shown in Fig. I, which is self explanatory. If we plot the grid potentials as abscissae and the plate current as ordinates, the curve obtained is called the characteristic. Due to the fact that the plate current as well as the grid current was so sensitive to small changes in the temperature of the filament, it was necessary to keep the heat- ing current very constant. Large storage cells, well insu- lated from the ground, were used for this purpose. A large resistance was placed in the external circuit, so that a small variation in the resistance of the filament would not affect the current appreciably. The characteristic curves of three types of audions are shown in Figs. 3, 4 and 5. Audion no. I is an oscillion made by the DeForest Radio Telephone and Telegraph Co. Audion no. 2 of Fig. 4 is a W-type; 1 PHYS. REV., Vol. X., No. 2, p. 205. io 3 CARL ELI PIKE. [SECOND [SERIES. Audion no. 3 of Fig. 5 is a V-type instrument made by the Western Electric Co. It is noted that the plate current in the oscillion reaches its saturation value more abruptly than it does in either of the other two instruments. In the oscillion it is necessary to heat the filament to incandescence before the electrons are emitted, while in audion W and V the light from the filament was scarcely visible. Fig. 3. Audion no. 2, the W-type instrument, was used for the amplification of the photoelectric current, with an arrangement of apparatus shown in Fig. 2. Twenty- four volts were used in the secondary circuit and a hundred and twenty-five volts in the primary. The photoelectric cell used was a larger type of those made by Kunz in our laboratory. With 125 volts in the primary circuit, the drop of potential inside the audion was very small; measured with an electrometer it was found to be 0.56 volt for nearly the highest intensity of light incident on the photoelectric cell. Since the drop of potential between the grid and filament is very small in comparison to that across the terminals of the photoelectric cell, the photoelectric current is very nearly equal to what it would be if the audion were out of the circuit. The curve giving the relation be- tween the intensity of light and the photoelectric current is shown in Fig. 6. It is unfortunately not a straight line. If this were a straight line and if the portion of the characteristic curve of the audion, used for the amplification, were straight, then we would expect a straight line relation between the intensity of light and the amplified current, and the amplification iz/ii, the ratio of the secondary to the primary current would be constant, represented by a straight line parallel to the hori- AMPLIFICATION OF PHOTOELECTRIC CURRENT. 104 -3 -f Fig. 4. Fig. 5. CARL ELI PIKE. [SECOND [SERIES. zontal axis of Fig. 7. Instead of this straight line, the curve of Fig. 7 has been obtained for intensities varying from 3 to 30 candle meters. For the highest intensity the amplification is about 1750, for the smallest Fig. 6. intensity it is over 5,000; above an amplification of 4,000 the points ap- pear somewhat scattered around the curve, but this was only so because the primary current deflections of the Leeds and Northrup galvanometer, Fig. 7. G\ (with a figure of merit 3.74-io~ 9 for the scale distance used), were very small. If the primary or photoelectric current i is zero, there is already a large current through the secondary galvanometer with a AMPLIFICATION OF PHOTOELECTRIC CURRENT. IO6 figure of merit 2.g-io~ 6 . It goes without saying that this "dark" cur- rent was subtracted from that current which was obtained in the galvan- ometer, Gz, when the photoelectric cell was under the action of light. The difference between the two deflections was proportional to the cur- rent i z . The deflections of the galvanometers were very steady and could easily be repeated. Table I. gives the data that have been plotted in Fig. 7. A satisfactory theory of the audion, based upon the motion, accumulation and absorption of electrons has not yet been given. The current amplification can therefore not yet be determined theoretically. But we can find a simple expression for the amplification, namely, iz/ii in the following way, which involves only Ohm's law and the experi- mental relation between the plate current and the grid potential ; as long as we restrict the amplification to the straight portion of the character- istic iz = Cpi, we get the following equations. RQ + RI The amplification is therefore constant if C and 'Ri are constants, that is, if the straight part of the characteristic is used and if the resistance R! be- ^__^ tween the filament and the r~ T~a ~L grid is constant. For large "I-H-M !N-l-H-H-M-H-M-l[ jy, ()) rt |j amplifications C and RI have to be large. A different principle has recently been indicated by A. W. Hull, 1 of the General Electric Company, for the Fig. 8. amplification of small cur- rents. By a proper choice of the potentials, the electrons emitted from the incandescent filament pass through the grid and strike the plate where they are reflected. A system of this kind, shown in Fig. 8, presents a negative resistance r between the points a and b. If we place a photo-electric cell with the positive resistance R in parallel with f, then we get; i P. I. R. E., February, 1918. CARL ELI PIKE. TABLE I. [SECOND [SERIES. Increase in