-NRLF B 4 E52 EEb v. f 4T ; < ; ' ! GIFT OF II '- ''**' 1 * m -.. _..- V *^ P l ;1 UNIVERSITY SOME CONTRIBUTIONS FROM THE LABORATORY OF PHYSICS OF THE UNIVERSITY OF ILLINOIS \V URBANA, ILLINOIS ^ 1914 O c P ^ .. r >> 58; 5 . 3 SOME CONTRIBUTIONS FROM THE LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS TABLE OF CONTENTS Introduction Note on the History of the Department of Physics at the University of Illinois. A. P. Carman The Design of a Physical Laboratory. Reprinted from The Brickbuilder, Janu- ary, 1912. A. P. Carman A Spontaneous Electromotive Force in Cells of Alkali Metals. Reprinted from the Physical Review, September, 1912. J. W. Woodrow Properties of the Wehnelt Cathode Rays. Reprinted from the Transactions of the American Institute of Electrical Engineers, October, 1912. C. T. Knipp lonization of Potassium Vapor by Ultra-Violet Light. Reprinted from the Phys- ical Review, October, 1912. S. H. Anderson The Magnetization of Heusler Alloys as a Function of the Temperature and Cal- culation of the Intrinsic Magnetic Field. Reprinted from the Physical Re- view, October, 1912. P. W. Gumaer A Simple Discharge Tube for Demonstration Purposes. Reprinted from Science, December 13, 1912. C. T. Knipp Determination of Capacities by Means of Conjugate Functions. Reprinted from Physical Review, December, 1912. J. W. Woodrow The Projection of "The Guinea and the Feather" Experiment. Reprinted from School Science and Mathematics, Vol. 13, 1913. A. P. Carman Some Recent Physical Theory. Reprinted from School Science and Mathematics, Vol. 13, 1913. A. P. Carman Determination Theorique de la Variation de la Masse de L'Electron en Fonction de la Vitesse. Abstract in Archives des Sciences physiques et naturelles, January, 1913. J. Kunz 2 UNIVERSITY OF ILLINOIS The Velocity of Electrons in the Photo-Electric Effect, as a Function of the Wave Lengths of the Light. Reprinted from the Physical Review, January, 1913. D. W. Cornelius lonization of Potassium Vapor by Ultra-Violet Light. Reprinted from the Phys- ical Review, March, 1913. S. H. Anderson Rectifying Properties of a Photo-Electric Cell. Reprinted from the Physical Re- view, March, 1913. S. H. Anderson Air Currents and Their Relation to the Acoustical Properties of Auditoriums. Reprinted from the Engineering Record, March 8, 1913. F. R. Watson Conditions .of Sensibility of Photo-Electric Cells with Alkali Metals and Hydro- gen. Reprinted from the Physical Review, April, 1913. J. G. Kemp The Use of Sounding-Boards in an Auditorium. Reprinted from The Brick- builder, June, 1913. F. R. Watson On the Beaded Character of the Cathode Ray Line as Revealed by Instantaneous Photographs taken at Short Range. Reprinted from the Physical Review, July, 1913- C. T. Knipp On the Present Theory of Magnetism and the Periodic System of Chemical Ele- ments. Abstract from "Original Communications," Eighth International Con- gress of Applied Chemistry, August, 1913. J. Kunz The Use of the Photo-Electric Cell in Stellar Photometry. Reprinted from the Astrophysical Journal, September, 1913. W. F. Schulz Thermal and Electrical Conductivities of the Alkali Metals. Reprinted from the Physical Review, September, 1913. J. W. Hornbeck A Determination of e/m and v by the Measurement of a Helix of Wehnelt Cathode Rays. Reprinted from the Physical Review, October, 1913. J. B'. Nathanson On the Use of Sealing Wax as a Source of Lime for the Wehnelt Cathode. Re- printed from the American Journal of Science, December, 1913. Nellie M. Hornor Acoustical Effect of Fi reproofed Cotton-Flannel Sound Absorbers. Reprinted from Engineering News, January 29, 1914. F. R. Watson A Determination of the Sun's Temperature. Reprinted from the Astrophysical Journal, May, 1914. G. A. Shook DEPARTMENT OF PHYS'ICS THE ELECTRICAL MEASUREMENT LABORATORY For advanced students for magnetic and electrical work for high precision. Calibration standards are kept connected for use in a special even temperature room. ONE OF THE SMALL LABORATORIES FOR SPECIAL EXPERIMENTS AND RESEARCH These laboratories are supplied with water, gas, compressed air and experi- mental electrical circuits, and double shades for darkening. There are twenty-five similar laboratories, '***' triflVERSITY OF ILLINOIS O < U S S ^ w DEPARTMENT OF PHYSICS NOTE ON THE HISTORY OF THE WORK IN PHYSICS AT THE UNIVERSITY OF ILLINOIS The instruction in physics at the University of Illinois was for years connected with the Mechanical Engineering Department. Professor S. W. Robinson who was the Professor of Mechanical Engineering from 1870 to 1878, taught physics also. From various pieces of apparatus which he devised and made, remains of which are stiil in the cabinets of the department, we know that there was a spirit of investigation even at that early date. Professor Robinson was succeeded by Professor S. H. Peabody who taught both mechanical engineering and physics until elected executive head of the University. For a time after this the instruction seems to have been irregular, at one time being connected with the department of Mining Engineering. In 1889 Samuel W. Strat- ton, the present director of the Bureau of Standards at Washington, was made Professor of Physics and reorganized the work on a modern basis. Professor Stratton was a graduate of the University in mechani- cal engineering and had also been instructor in the architectural and preparatory departments. He brought a knowledge of practical me- chanics and pieces of apparatus are still in the department which he made for the work. In 1892 Professor Stratton went to the University of Chicago and was succeeded by Dr. D. W. Shea. Professor Stratton started, in connection with the Physics Department, courses in electrical engineering and purchased imore or less apparatus for this work. The University began to get larger appropriations from the State for main- tenance and Professor Shea continued the development of the electrical engineering work by adding much apparatus and also strengthening the instructional work in physics by more equipment adapted to the newer laboratory methods. The opening of Engineering Hall in the fall of 1894 removed the Department of Physics from the limited quarters which it had occupied in University Hall for many years. The three floors of the north wing of the Engineering Hall gave to the department a floor space of about eleven thousand square feet and the rooms were well equipped for the instructional side of the work in physics. The dynamo laboratory and other testing rooms for the electrical engineering work remained in the basement of University Hall until the fall of 1898 when the present Electrical Engineering Laboratory was completed in connection with an appropriation for the new heating and power plant for the University. In December, 1895, Professor Shea severed his connection with the University to become the first professor of physics in the Catholic University of America at Washington, D. C. Albert P. 6 UNIVERSITY OF ILLINOIS Carman was elected to the professorship of physics and began his services at the University in September 1896. The work of electrical engi- neering was not separated administratively from the Department of Physics until the fall of 1898. This separation gave better opportunity for developing the work in physics. The equipment of the department was within the next few years practically all replaced by new and modern apparatus. The rapid increase in the number of engineering students taking required courses in physics made it necessary not only to replace the old equipment, but also to add very largely to the equipment and also to the number of instructors in the department. This expansion ab- sorbed the energy of the department for a number of years. In 1904- 1905 a movement was started to obtain a new and modern laboratory for the department. The legislature of Illinois was asked in 1906 to make an appropriation for a laboratory but other interests seemed more urgent. The request was renewed to the following legislature and at this time an appropriation was made for buying the present site for a new building. In the following legislature, that is, in 1907, an appropriation of $250,000 was made for a physics building. The contract for this building was let in July 1908, and the building was completed and dedicated on November 27, 1909. The American Physical Society made this the occasion for meeting in the new laboratory for the Thanksgiving meeting of that year. The program of the dedication shows this and also the prominent part that the address and lectures of Professor A. G. Webster had at this dedication. While the new laboratory with its excellent facilities and equip- ment stimulated the research work of the department, yet this work had already shown increasing activity by the publications of several years; and indeed the demands of physical research were in no small part re- sponsible for the new building. Below is given a list of publications by members of the department, beginning with 1909 to the close of 1913: "On the Rate of Formation of Carbon Monoxide in Gas Producers," by J. K. Clement, University of Illinois Engineering Experiment Station, Bulletin No. 30, 1909. "The Time Rate of Gas Reactions of CO 2 ," by J. K. Clement, University of Illinois Engineering Experiment Station Bulletin No. 30. "A Simple Cloud Apparatus," by C. T. Knipp, Science, December, 1909. "A Substitute for Lampblack," by F. R. Watson, School Science and Mathe- matics, Vol. 9, 1909. "Architectural Acoustics," by F. R. Watson, Technograph, Vol. 23, 1909. "The Effect of a Magnetic Field upon the Absorption Spectra of Certain Rare Earths," by W. F. Schulz, Astrophysical Journal, December, 1909. "On the Electron Theory of Thermal Radiation for Small Values of (N T)," by J. Kunz, Physical Review, May, 1909. "On the Photoelectric Properties of Sodium Potassium Alloy," by J. Kunz, Physical Review, August, 1909. "On the Photoelectric Effect of Sodium Potassium Alloy and its Bearing on the Structure of the Ether," by J. Kunz, Physical Review, September, 1909. DEPARTMENT OF PHYSICS 7 "The Thermal Conductivity of Fire-Clay at High Temperatures," by J. K. Clement and W. L. Egy, University of Illinois Engineering Experiment Station, Bulletin No. 36, 1909. "The Effect of Pressure on the Electrolytic Rectifier," by A. P. Carman and G. J. Balzer, Physical Review, February, 1910. "The Effect of Pressure on the Aluminum Rectifier," by A. P. Carman and G. J. Balzer, Physical Review, June, 1910. "The Instruction of Large University Classes," by A. P. Carman and F. R. Watson, Science, December, 1910. "A Convenient Form of Quartz Tube Mercury Lamp," by C. T. Knipp, Physical Review, May, 1910. "Temperature and Potential-Pressure Relations in the Mercury Arc," by C. T. Knipp, Physical Review, August, 1910. "An Apparatus for Measuring Sound," by F. R. Watson, Physical Review, January, 1910. "Effect of Surface Tension upon a Falling Jet of Water," by F. R. Watson, Physical Review, February, 1910. "A Peculiar Heat Phenomenon," by F. R. Watson, Science, Vol. XXXII. "Manual of Experiments in General Physics for Engineering Students," by W. F. Schultz, Flanigan-Pearson Co., Champaign, Illinois, June, 1910. "The Absolute Values of the Moments of the Elementary Magnets of Iron, Nickel and Magnetite," by Jakob Kunz, Physical Review, March, 1910. "On the Electromagnetic Emission Theory of Light," by J. Kunz, American Journal of Science, November, 1910. "On the Initial Velocity of Electrons as a Function of the Wavelength in the Photoelectric Effect," by J. Kunz, Physical Review, November, 1910. "Magnetic Properties of Heusler Alloys," by E. B. Stephenson, Physical Re- view, September, 1910. "The Nature of Spark Discharge at Very Small Distances," by E. H. Wil- liams, Physical Review, September, 1910. "Comparison of the Magnetic Properties of Nickel and Iron," by E. H. Wil- liams, Electrical Review and Western Electrician. December 3, 1910. "Magnetic Properties of Heusler Alloys," by E. B. Stephenson, Illinois Engi- neering Experiment Station, Bulletin No. 47, 1910. "The Design of a Physical Laboratory," by A. P. Carman, The Brickbuilder, December, 1911. "Rays of Positive Electricity from the Wehnelt Cathode," by C. T. Knipp, Philosophical Magazine, December, 1911. "On the Positive Potential of Metals in the Photoelectric Effect and the Determination of the Wave-Length Equivalent of Roentgen Rays," by J. Kunz, Physical Review, September, 1911. "Echoes in an Auditorium," by F. R. Watson, Physical Review, February, 1911. "Musical Echoes," by F. R. Watson, Science, October 6, 1911. "Laboratory Physics," by T. S. Taylor, Manual of 225 pages for Sophomore first year laboratory work, Gazette, Champaign, Illinois, 1911. "On the lonization of Various Gases by the Alpha Particles from Polonium," by T. S. Taylor, Philosophical Magazine, April, 1911. "Some Tests on Certain Electrical Insulators at High Temperatures," by W. W. Stiffler, Physical Review, April, 1911. 8 UNIVERSITY OF ILLINOIS "The Magnetization of Cobalt as a Function of the Temperature and the Determination of its Intrinsic Magnetic Field," by W. W. Stiffler, Physical Re- view, October, 1911. "Increase of Magnetic Induction in Nickel Bars Due to Transverse Joints," by E. H. Williams, Physical Review, July, 1911. "Spark Discharge at Very Small Distances," by E. H. Williams, Physical Re- view, June, 1911. "Effect of Frequency on the Capacity of a Condenser, with Kerosene for the Dielectric," by S. H. Anderson, Physical Review, January, 1912. "lonization and Photoelectric Properties of Vapors of Alkali Metals," by S. H. Anderson, Physical Review, October, 1912. "Magnetism and Electricity," by A. P. Carman, Part of a Text-Book of Physics, edited by A. W. Duff, Philadelphia, 1912. "The Magnetization of Heusler Alloys as a Function of the Temperature and Calculation of the Intrinsic Magnetic Field," by P. W. Gumaer, Physical Review, October, 1912. "Uber Photoelectrische Indicatoren fur electromagnetische Wellen," (with J. Kunz), by J. G. Kemp, Jahrbuch der drahtlosen Telegraphic und Telephonic, 1912. "On the Production of a Helix of Rays from the Wehnelt Cathode," by C. T. Knipp, Physical Review, January, 1912. "Rays of Positive Electricity from the Wehnelt Cathode," by C. T. Knipp, Physical Review, March, 1912. "Properties of the Wehnelt Cathode Rays," by C. T. Knipp, Transactions of American Institute of Electrical Engineers, October, 1912. "A Simple Discharge Tube for Demonstration Purposes," by C. T. Knipp, Science, December 13, 1912. "On the Present Theory of Magnetism and the Periodic System of Chemical Elements," by J. Kunz, 8th International Congress of Applied Chemistry, Volume XXII. "Radiation Pyrometry," by G. A. Shook, Metallurgical and Chemical Engi- neering, April i, 1912. "Rechnungsapparat fur die Bestimmung von thermodynamischen Tempera- turen," by G. A. Shook, Physikalische Zeitschrift, August, 1912. "The Number of Ions Produced by an Alpha Particle," by T. S. Taylor, Philosophical Magazine, April, 1912. "The Electron Theory of Magnetism," by E. H. Williams, University of Illinois Engineering Experiment Station, Bulletin No. 62, 1912. "A Spontaneous Electromotive Force in Cells of Alkali Metals," by J. W. Woodrow, Physical Review, September, 1912. "Determination of Capacities by Means of Conjugate Functions," by J. W. Woodrow, Physical Review, December, 1912. "Rectifying Properties of a Photoelectric Cell," by S. H. Anderson, Physical Review, March, 1913. "lonization of Potassium Vapor by Ultra-Violet Light," by S. H. Anderson, Physical Review, March, 1913. "Recent Physical Theory," by A. P. Carman, School Science, January, 1913. "The Velocity of Electrons in the Photo-electric Effect as a Function of the Wave Lengths of the Light," by D. W. Cornelius, Physical Review, January, 1913. "A Substitute for a Bronson Resistance," by J. G. Kemp and D. W. Cornelius, Physical Review, January, 1913. DEPARTMENT OF PHYSICS 9 "Conditions of Sensibility of Photo-electric Cells with Alkali Metals and Hy- drogen," by J. G. Kemp, Physical Review, April, 1913. "On the Beaded Character of the Deflected Cathode Ray Line as Revealed by Instantaneous Photographs Taken at Short Range," by C. T. Knipp, Physical Re- view, April, 1913. "Determination theoretique de la variation de la masse de 1'electron en fonction de la vitesse," by J. Kunz, Archives des Sciences Physique et Naturelles, 1913. "Contributions a la theorie du magnetisme," Journal de physique, 1913. "Effect of Gas Currents on Sound," by F. R. Watson, Physical Review, Jan- uary, 1913. "The Use of Sounding Boards in an Auditorium," by F. R. Watson, Physical Review, March, 1913. "Air Currents and the Acoustics of Auditoriums," by F. R. Watson, Engineer- ing Record, March 8, 1913. 10 UNIVERSITY OF ILLINOIS 44-0 X . n D ELECTRICAL MEAfUTJLMLNU LABORATORY OF PHYSICS FIRST FLOOR a en GENERAL PHYJ1GS LABORATORY X CZl i MlilM APPARATUS < r nnnn. ADMINlfiMION. orncr. ttttUUg 20-li"xl9-9" 12OOM. T2ECITATION 23 : 1V X 19-9" ROOM N0.6. LABORATORY LABORATORY IS'-IO'X 19'-9"| 2b L li'X .19'-9' NO. 1 2. m NO 13. LABORATORY OF PHYSICS THIRD FLOOR DEPARTMENT OF PHYSICS It 65 APPy*xm ZOOM n n n n JR n n n n a LABORATORY OF PHYSICS SECOND FLOOR LABORATORY OF PHYSICS FOURTH FLOOR 12 UNIVERSITY OF ILLINOIS THE DESIGN OF A PHYSICAL LABORATORY (Reprinted from The Brickbuilder, January, 1912) ALBERT P. CARMAN. The design of a highly specialized building like a university physical laboratory presents many problems outside the experience of the general architect. The literature on the design of such buildings is very meager. A number of laboratories have been described in a general way, but often with particular emphasis on fittings and apparatus and with little, if any, -discussion of the problems supposed to be solved in the design. The following article, it is hoped, will help fill this deficiency. The writer had the responsibility of making specifications for the design of a physical laboratory for the University of Illinois, and was in consultation with architects and superintendents during the erection and equipping of the building. It is believed that an explanation of the plans finally used will aid those who have to design this type of building. About twenty leading physical laboratories in this- country were visited, and the floor plans of practically all of. the recent laboratories secured. Several months were spent in making floor plans after various schemes. In this preliminary work an architectural student was em- ployed to make drawings to exact scale. The possibilities and advantages of various schemes were thus made manifest, and the essential principles to be followed in the design became evident. In these preliminary studies as well as later, Prof. J. M. White of the Department of Architecture and Prof. C. T. Knipp of the Department of Physics were active workers. This preliminary work was done before the election of the architect, there being a delay of several months in his election, and the result was that a very complete and definite list of conditions was furnished him. The architect (Mr. W. C. Zimmerman of Chicago), found the general results of these preliminary studies very helpful, and nowhere asked for a sacri- fice of technical requirements to get architectural effects. The character of the work in physics, which consists of the usual undergraduate courses, and of a considerable and growing amount of graduate work and of investigation, fixed the number and general char- acter of the rooms desired. The site was also fixed, a rectangular space of about 250 feet square with a south front for the building. Fortunately or unfortunately, the University has adopted no style of architecture, so there was no question of adapting ecclesiastical windows or projecting buttresses of classical columns to the requirements of unrestricted light. Such architectural styles present very difficult problems in laboratory design. They have been solved more or less successfully, but the difH- DEPARTMENT OF PHYSICS 13 culty is such that we cannot wonder that more than one professor has suggested that the best style for a laboratory would be that of the com- mon workshop, and perhaps with saw-tooth roof construction. But efficiency is not in conflict with dignified architecture, and a university physical laboratory should be an attractive building to conform to the importance of the science in university work. The exterior of a physical laboratory is important to the man of physics, principally in its allowing a convenient window spacing, with unobstructed light, as well as being inexpensive, so that no interior convenience need be sacrificed. The style chosen as appropriate to our surroundings fitted our requirements and money, and gave us a dignified and pleasing exterior without sacrificing interior plans. The elevation and the floor plans discussed below are shown in the accompanying illustrations. Freedom from mechanical disturbances is of such obvious impor- tance for much of the work in physics that it received early consideration. Since the laboratory is for university instruction the location is neces- sarily central, and that means in the midst of various activities which may cause vibration. The first thing decided was to use extra heavy masonry walls and as far as possible to carry the floors on masonry walls rather than on steel columns. This involves many cross walls which run the full length of the building and give a rigid cellular design as seen in the floor plans. Over three million bricks were used, probably twenty- five per cent more than would be used with steel columns in a building of this size. Next came the effect of room arrangement and of equipment on stability. To avoid the disturbances caused by the movement of large classes of vigorous students the large laboratories and the class rooms are put on the west side of the building. Most of the students naturally use the west entrance, so that this design minimizes the travel across the building. The east side of the building is thus given over to the twenty-five smaller laboratories which are used by advanced students and individual investigators for the more delicate experiments. This side of the building is much heavier in construction owing to numbers of interior masonry walls. An equally important question was the location of moving machines. The ventilating fans, the liquid air plant and department machine shop are placed in an annex building which has a foundation separate from that of the main building. A hydraulic plunger elevator was installed partly on account of its simplicity and safety, but mainly because it in- troduced no rotating machinery. All the rotating machinery in the main building is concentrated in the students' workshop at the northeast cor- ner. The floor of this room is a thick block of reinforced concrete floated on 18 inches of sand and is independent of the walls and founda- tions. On this are mounted several machine tools with shafting and motor for the use of instructors and advanced students. This method of isolating machinery has been used in several laboratories and found 14 UNIVERSITY OF ILLINOIS satisfactory. It would of course be easy to restrict work in this shop at times if any particular experimental work was disturbed, but our ex- perience indicates that this will rarely occur. As heat and electric power come from the University power plant we have had no problem with boilers and prime-motors. An equally important question was the use of the basement. Many professors regard the basement as the choicest room on account of its stability. That it is not necessary to go to the basement for stability is shown by the two fine research laboratories in Washington, the Geo- physical Laboratory and the Laboratory of the Bureau of Standards. These laboratories do not depend upon the basement for delicate ex- perimental work. The objections to basement rooms are that they are not cheerful and that they are liable to be damp at certain seasons of the year. In the level prairie country with the black soil of the "corn belt," basement rooms are certainly not desirable where long hours must be spent in experimental work. While we have a large basement ce- mented throughout, part of it is cut by the ventilating ducts and the piping, and part is used for even-temperature rooms, a large battery room, and storage room, much needed in working laboratories. All the first floor laboratories and the lecture room desks have independent masonry piers for experiments. The wall brackets have, however, been found equally stable. Even on the upper floors the wall brackets have been satisfactory for all general purposes and are particularly good near the intersections with the cross walls. There are occasionally demands of stability made by physical ex- periments which test to the limit the standard masonry pier. To meet this exceptional but important demand three special piers were con- structed. A heavy block of concrete was built on a thick bed of loose gravel. By using oil cloth over the gravel the concrete formed without becoming part of the gravel, and was thus "floated" on the gravel. The pier was then erected in this floating foundation. The loose gravel trans- mits few if any vibrations and the inertia of the heavy concrete founda- tion and pier is an additional protection against vibrations. A pier of this kind will stand the test of a free mercury surface. While stability is demanded in a physical laboratory, the question of convenient arrangements, service rooms and "circulation" or ready access is none the less important in a laboratory as large as this one. The first question in arrangement was the location of the large experi- mental lecture room. A lecture room requires higher ceilings than the ordinary room on account of the raised seats and its size. It must be convenient to a preparation room and the apparatus cabinets, and should be easily accessible to the auditors. To obtain the higher ceiling without breaking floor levels the lecture room is often put on the top floor. This would have involved in our case a climb of two or perhaps three flights of stairs which was undesirable for several reasons. The problem was DEPARTMENT OF PHYSICS 15 finally solved by using the court between the wings for two lecture rooms and a preparation room. The access is easy and the location re- duces the disturbance of the coming and going to a minimum. The lighting is by skylights with a north exposure and no side-lights ; allow- ing the room to be quickly and completely darkened by horizontal screens rolling on tracks between the skylights and the glass ceiling. The size of the lecture room forms a question on which there is evidently .much difference of opinion. After a thorough test it was decided that 50 feet should be the maximum distance of any seat from the lecture desk for an experimental lecture. Using a standard opera chair with folding tablet arm there are 265 seats within this radius, which number is ample since, for teaching efficiency, a lecture section of over 200 is undesirable. The second lecture room seats 120 and shares the preparation room with the large lecture room. An apparently minor point that caused much thought in the lecture room design was the position of the entrance. A rear entrance is undesirable because it is not in full view of the lecturer and so encourages tardiness. The entrance should be placed so as not to interfere with the passage from the desk to the preparation room. In a physics lecture roo,m it is desirable to have a diagonal curtain across one front corner so that a lantern can be operated for projecting ex- periments. These requirements are met very satisfactorily in the larger lecture room and fairly so in the smaller lecture rooms. There is a scheme used in some foreign laboratories of having the entrance to the preparation room and cabinets directly back of the lecture desk, with sliding blackboards and a projection curtain coming down over this entrance. It seems, however, better to keep the needed blackboard, and curtain independent of an entrance. The location and arrangement of the apparatus cabinets is a special feature of the design. These are placed in the north central part of the building and extend through three stories. The principle of the library stack is used, a mezzanine floor being introduced on each story. This scheme practically doubles the available apparatus room. These stacks are accessible from each corridor by a special stairway and by an eleva- tor. The elevator shaft runs from the unpacking room in the base,ment to the fourth floor and has openings to the main corridor on each floor, and also to each of the six floors with apparatus stacks. By using large rubber-tired trucks which can be run on the elevator it is easy to transfer heavy apparatus to any part of the building. The central location of these apparatus stacks makes them convenient to all the working rooms of the building. Indeed the preparation rooms for the lecture rooms and for the large laboratories on the second and third floors open directly into these stacks. In addition to these central cases each small labora- tory is fitted with a case for the apparatus and supplies which are in current use in that room. For each large laboratory there is a preparation room supplied with facilities for adjusting apparatus and making minor repairs, and also an l6 UNIVERSITY OF ILLINOIS administration office with assistants' desks where reports are corrected and records kept. On each floor there is a chemical room and one or more photographic rooms. Interior dark rooms are also found in several of the smaller laboratories. Some of these laboratories are fitted with double curtains held in place by deep side slots so that the room can be easily darkened for ordinary purposes. The device of using double curtains bound together but mounted on separate spring rollers fixed vertically over each other is due to Prof. D. C. Miller. It is inexpensive and satisfactory. The class rooms, seminary room, offices, coat rooms, etc., involve no questions peculiar to laboratory design. The experimental electric circuits and switchboards, and the distribution of gas, water, and com- pressed air are important features in a modern laboratory, but they are perhaps more in the nature of equipment rather than subjects of design. For the extension of this wiring and piping either temporary or perma- nent accessible shafts are provided in all parts of the building. This provision cannot be neglected in a fire-proof building. The fourth floor is also completely finished. It contains extensive photographic rooms with a large north skylight and rooms which are available for various experiments in light, sound, and electric waves. There are no special points of design involved in the planning of this floor. In addition to the question of general design in the planning of a laboratory there arise many questions in the design of the individual rooms and in their fittings, but these questions of detail are beyond the purpose of this paper. DEPARTMENT OF PHYSICS en js en * <0 " & j $ C .ti _ en 5 6 . C en O * HJS o 8 JAY W. WOODROW. [VoL. XXXV. platinum. After four months these cells still show a perfectly pure alkali-metal surface. That is, a small beam of light is so reflected from the metal that one cannot see the spot where it strikes the surface. Time has not permitted a further investigation to determine whether this formation of a film was due to the gases contained in the aluminium electrode or to some action betw r een the alkali vapor and this electrode. No attempt has been made to explain all the phenomena described here. However, all the results point to the conclusion that some sort of positively charged particles are given off by the alkali metals in a high vacuum. As Dr. Anderson in a paper which is to appear later has shown that at the high temperatures this emission of positive electricity is so great as to counterbalance the. ordinary photo-electric effect in the light, we conclude that this action is taking place in the light as well as when screened from light but is overbalanced by the emission of negatively charged electrons at ordinary temperatures in the latter case. If we consider the current given by these cells as due to positive par- ticles emitted from the surface of the metal, the number leaving the surface can be computed. For we have that . n = 7 xx 20 = X -3X where n is the number leaving the surface per second, i is the current, and e is the charge on each carrier. At a temperature of 25 C. the current was found to be i = 1.9 X io- 16 E.M.U. Taking e to be 1.5 X io~ 20 , this gives for the number leaving the surface per second, X IP" 15 1.5 X io- It is interesting to compare this with the total number of atoms in the surface layer of the alkali metal. An approximate value of the average area of cross-section of the atom in the alloy used is 1.7 X io~ 15 sq. cm. The area of the surface was 8.4 sq. cm. so that the total number in the surface layer was rdHo^ - s x I0 ' 6 - - Hence, the ratio of the total number of atoms in the surface layer to the number of particles leaving this surface per second is 1.3 X io 5 No. 3.J SPONTANEOUS ELECTROMOTIVE-FORCE. 2CX) That is, if the current is considered as due to positive particles shot out from the metal, only one atom out of 3.8 X io 10 of those on the surface layer would be required to emit a positive particle per second in order to account for the total current. At 120 C. the current was 2.6 X io~ 13 E.M.U., and consequently, n = 1.7 X io 7 . The ratio of the total number of atoms in the surface layer of positive particles emitted per second would be 5 X io 15 ITlotf = 3 x I0 ' These results seem to indicate that only a very small proportion of the atoms are active and that the number increases with the temperature. If it can be proved that this current is due to positive particles shot off from the active atoms (or molecules), it will give a direct proof of the theory of radiation which assumes that only a small proportion of the molecules of a radiating body are active. These investigations are to be continued further in order to investigate more thoroughly the nature of this positive emission and to determine the source of the energy. The present investigation has been carried out during the past year under the direction of Dr. Kunz, whom the author wishes to thank most heartily for his many helpful suggestions and for his never-failing interest and aid in the progress of the work. LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS, URB ANA- CHAMPAIGN, ILLINOIS A paper presented at the Urbana Section meeting of the American Institute of Electrical Engineers, Urbana, 111., Feb. 21, 1912. Copyright 1912. By A. I. E. E. (Subject to final revision, for the Transactions'). PROPERTIES OF THE WEHNELT CATHODE RAYS BY C. T. KNIPP The discharge of electricity through gases is a subject that has had a most wonderful growth, a growth possibly greater than that of any other single division in physics. With the discovery of cathode rays, X-rays, radio-activity, and rays of positive electricity, a new era was begun. The cathode rays were the first of the above to be brought to our attention, how- ever, but little was known of their properties until the researches of the last decade. About fifteen years ago the wonderful X- or Roentgen rays were discovered. A few years later came that almost revolutionizing discovery of radio-activity, revo- lutionizing because we are obliged to change our conceptions regarding the molecule and atom. Another of equal importance because of its bearing upon chemical composition, is afforded by J. J. Thomson's recent investigations on rays of positive electricity. These avenues in physical science that have been opened by the researches of such eminent physicists as Crookes, Roentgen, Thomson, Rutherford, the Curies, Webnelt and others, have played, and will play a most important part on the problems of the consititution of matter and the nature of electricity. It is safe to say that we know more nearly what is going on when elec- tricity passes through a gas than when it passes through either liquids or solids. Let us take, for instance, an ordinary discharge tube (exhibiting tube) connected to a quick acting pump (e.g., the Gaede). First notice the form of the tube and its construction. This one is 1.5 meters long, and about four cm. in diameter. The two electrodes are flat disks of aluminum about two cm. in diameter 1883 *"" ,:S-- , , d / 2S' d 00 5 i 2. A? ^ ID ^-^"2 V ^ 6 ? ' u \ r^' t - 8. At 150 light has practically no effect on the emission of electrons from potassium. 9. By comparing the currents for different temperatures in tube No. 2, with potassium electrode, it is found that the greatest relative effect of light on the emission of electrons is at 25. 10. The maximum vapor pressure possible for potassium at 25 has been found to be 0.0587 mm. The author wishes to express his indebtedness to Professor A. P. Carman and the department of physics for the facilities for this investiga- tion, and to Professor Jakob Kunz who suggested the problem and has given many valuable suggestions. LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS, May, 1912. THE MAGNETIZATION OF HEUSLER ALLOYS AS A FUNCTION OF THE TEMPERATURE AND CALCULATION OF THE INTRINSIC MAGNETIC FIELD BY PERCY WILCOX GUMAER (Reprinted from the PHYSICAL REVIEW, Vol. XXXV.. No. 4, Oct.. 1912.1 THE MAGNETIZATION OF HEUSLER ALLOYS AS A FUNCTION OF THE TEMPERATURE AND CALCULATION OF THE INTRINSIC MAGNETIC FIELD. BY PERCY WILCOX GUMAER. THE magnetic alloys of manganese are composed of metals which ordinarily are non-magnetic. Manganese itself is not only non- magnetic, but a small per cent of it will reduce the magnetic properties of iron. It is probable that the explanation of these magnetic alloys will add considerable to our understanding of the ultimate nature of magnetism. Recent developments in the electron theory of magnetism have opened up a means of studying the molecular structure of the alloys. The present investigation was undertaken with two objects in view, first: to study the effect of temperature upon the saturation value of the intensity of magnetization. Then, to determine, if possible, from the data obtained, the structure of the molecular magnets. METHOD. To determine the saturation value of the intensity of magnetization the method used by Weiss 1 and Stifler 2 was chosen. A ballistic galva- nometer was connected in series with a helix placed in a strong magnetic field. An ellipsoid of the alloy to be tested was placed in the center of this helix and the deflection of the galvanometer was observed as the ellipsoid was, quickly, pushed out. The deflection of the galvanometer was then compared to that obtained from the current induced in the secondary of a standard helix which was included in the circuit. The intensity of magnetization I can be determined from the relation : '' - * where k = a constant depending upon the dimensions of the helix and of the standard helix. v = the volume of the ellipsoid. i = current in the primary of the standard helix. d f = deflection due to induced current in the standard helix. d = deflection when ellipsoid is removed from the helix. 1 Archives des Sciences, ser. 4, 29, pp. 204 (1910). *PHYS. REV., Vol. 33, p. 268 (1911). No. 4. J THE MAGNETIZATION OF HEUSLER ALLOYS. 289 The ellipsoid and helix were surrounded by a coil of German silver wire, by means of which the desired temperature was obtained. To measure the temperature of the ellipsoid inside the helix a copper-con- stantan thermo-couple was used. The hot junction was placed in a hard glass tube 3 mm. in diameter and 26 cm. long. Inside the tube the wires were separated by mica strips, outside by 1/16 rubber tubing. The thermo-couple was calibrated by observing the E.M.F. of the couple when the hot junction was at a known temperature. The tem- perature of steam and the freezing points of metals were used for the calibration, as follows: Zn 419.4 C., Cd 321.0 C., Sn 231.9 C., steam 1 00 C. Using the method of least squares the constants of the equation E = at + bt 2 + ct* were determined and the equation becomes E = 3.747* -f- .00375/2 + .00000164^. The galvanometer used was a Leeds & Northrup silver suspension instrument. It had a resistance of 25.6 ohms, a ballistic sensibility of 31.8 mm. per micro-coulomb on open circuit, with a scale distance of 50 cm., and a period of 11.2 seconds on open circuit. At a scale distance of 6 meters and the deflection could be read to 0.5 mm. The ellipsoid was inserted directly into the tube forming the core of the helix. It was moved along by pushing with a small glass rod in one end and with the tube containing the thermo-couple in the other end. By this method the diameter of the helix could be decreased by half, which increased the sensitiveness considerably. The induction helix was wound upon a thin-walled glass tube 45 cm. long and 0.5 cm. outside diameter. Three layers of number 36 silk- covered copper wire were used. The layers were separated by mica, and each layer was covered with a mixture of water glass and calcined magnesia. This mixture became very hard when dry and held the wires firmly in place even at high temperatures. A hard glass tube long enough to reach to the end of the bore in the magnet was slipped over the helix coil. Thus the possibility of leakage from the heating circuit to the helix coil or lead-in wires was avoided. The heating coil consisted of one layer of 320 turns of number 16 German silver black enameled wire. The winding was done from the middle towards the ends so that the two halves were wound in opposite directions and opposed each other magnetically. As in the induction helix, a mixture of water glass and magnesia was used to hold the wires firmly in place. Since the length of the coil was 30 cm. the temperature gradient in the center was very small. The induction helix and heating coil were enclosed in a glass tube small 290 PERCY WILCOX GUMAER. [VOL. XXXV. enough to slide into the bore of the magnet. This tube was filled with calcined magnesia. Further heat insulation between the pole pieces was obtained by enclosing that part of the furnace in a fire clay cylinder filled with shredded asbestos. The magnetic field was obtained from a large DuBois electromagnet. A hole drilled through the core and pole pieces enabled the ellipsoid to be inserted into the helix. For the air gap used (6.2 cm.) the strength of the magnetic field in the center of the gap was calibrated in terms of the current in the coils. A magnetic balance was used to measure the strength of the field. DESCRIPTION OF SPECIMENS. The alloys were prepared by melting in a new graphite crucible heated in a gas furnace. The manganese and copper were put in first, and when they were thoroughly fused the aluminum was added. To insure a uniform mixture, the molten alloy was stirred with a graphite rod, and then quickly poured into vertical moulds. Care was taken to pour in a continuous stream so that the oxide formed on the surface would not injure the casting. The ellipsoids were obtained by grinding the castings with a properly shaped alundum wheel in a Universal Grinder. A projection of the shadow of the ellipsoids showed the cross-section to be fairly accurate. The dimensions and composition of the two ellipsoids are given as follows : Ellipsoid No. i. Ellipsoid No. a. Length 1.686 cm. 1.680 cm. Mean diameter 0.393 cm. 0.399 cm. Volume 0.1364 cu. cm. 0.1401 cu. cm. Mass 0.9487 gm. 1.0028 gm. Density 6.96 7.15 Copper 62.9 per cent. 61.95 per cent. M anganese 18.5 per cent. 21.9 per cent. Aluminum 15.1 per cent. 15.9 per cent. Undetermined 3.5 per cent. 0.25 per cent. PROCEDURE IN TAKING READINGS. After the heating current had been on for a time, sufficient to estab- lish temperature equilibrium, the ellipsoid was inserted into the core of the helix. It was moved along by pushing with the tube containing the thermo-couple from one end and with a glass rod from the other end. A mark on the glass rod indicated when the ellipsoid was in the No. 4.] THE MAGNETIZATION OF HEUSLER ALLOYS. 2 9 I center of the helix. When the temperature had ceased to increase the reading of the thermo-couple was taken, the magnetic field was thrown on and the deflection of the galvanometer was observed as the ellipsoid was quickly pushed out of the helix. A rapid movement of the ellipsoid was obtained by striking the end of the glass rod with a small piece of wood. The ellipsoid was now replaced in position, allowed to regain its former temperature and the reading repeated. As a rule three readings were taken for each field strength and the intensity of magnetization was calculated from a mean of the three deflections. At lower temperatures the deflections agreed to within I per cent, but in the neighborhood of the transformation temperature the agreement was not as close. For some of the readings taken above 300 the maxi- mum deflection was I cm. at a scale distance of 6 meters. The accuracy in this case was probably about 10 per cent. After each set of readings the galvanometer was calibrated by means of the standard helix. The current in the primary of the helix was read by a Weston milli-ammeter, which had been calibrated by comparison with a standard in- strument. The ratio i'ld' varied slightly as the temperature in- creased, due to the increased resistance of the helix coil at higher temperatures. As the heating coil was wound non- magnetically, it was not neces- sary to make any correction for it. Thermo-couple readings were taken just before the ellipsoid was pushed out of the helix. As the end of the tube contain- ing the thermo-couple was left Fi ^ open, and as the couple was within a millimeter of the end of the ellipsoid when readings were taken, it is quite probable that the temperature measured corresponded very accurately to the actual temperature of the ellipsoid. RESULTS. The first set of data obtained is apparently of little theoretical value. The curves (Fig. i) showing the specific intensity of magnetism a as a 25 IS Tempera 50 ure 100 \ '" ^ 00 \ 250 2 9 2 PERCY WIJjCOX GUMAER. [VOL. XXXV. function of the temperature are quite irregular, having a maximum at 140. Although it is possible that the irregularity of these curves is due to a defect in the apparatus, it is more probable that it is due to the unstable conditions of the alloys. The data were obtained with the alloys in the condition as cast and without previous heat treatment. 2.0 15 25- 2.0 15 Tempe -At-ure 50 IM ISO 90 250 50 100 > 150 2io 250 Fig. 2. Ellipsoid No. 1. Fig. 3. Ellipsoid No. 2. A new helix coil was now built and a series of readings taken at 320 indicated that the substance had become paramagnetic. Beginning at room temperature, the whole set of data was repeated and very regular curves were obtained, as shown in Figs, a and 3. These curves, showing . A^Xio 22 . Iron 2,120 756 C. 3,850 6,560,000 5.15 4.12 Cobalt 1 435 1 075 6 180 8 870 000 621 2 31 Nickel 570 376 12,700 6,350,000 3.65 1.56 Alloy No. 1 . Alloy No. 2 . 518 533 310 310 12,940 10,540 6,700,000 5,620,000 3.55 4.23 1.46 1.26 If we assume that there is one atom of manganese in the magnetic molecule then for alloy number one we have the relation wn where m H = weight of a hydrogen atom. w = 55 = atomic weight of manganese. n = 1.46' io 22 the number of magnetic molecules per cu. cm. d = density of alloy X per cent, of manganese in alloy. = 6.96-0.185. 6.96-0.185 m H = IO 22 = I.60-IQ- 24 . 1 R is the universal gas constant, and the value to be used is that corresponding to one molecule. 2 PHYS. REV., Vol. 30, p. 259 (1910). 1 PHYS. REV., Vol. 33, p. 268 (1911). 304 PERCY WILCOX GUMAER. [VOL. XXXV- This value of m H agrees almost exactly with 1 .61 IQ- 24 , the value obtained by Rutherford. From alloy number two we get m H = 2.I2-IO" 24 , which does not agree very closely. If e is the elementary charge of the hydrogen atom and a n is the chemical equivalent of hydrogen, then e = m H /a H . Using the values of m H obtained above we get from alloy number one e = i.54-io~ 20 and from alloy number two e = 2.04 -io~ 20 . We could have obtained, however, the same values by assuming that the magnetic molecule was composed of one atom of manganese and one atom of aluminium, or one atom of manganese and one atom of copper. Since a molecule must contain more than one atom, it is quite probable that the magnetic molecule is a composite molecule containing one atom of mangenese and one atom either of copper or of aluminium. This hypothesis would also account for the increase in the intensity of magnet- ism after chilling from a high temperature, as shown in Fig. 6. The chilling prevents one of the metals from crystallizing out and thus prevents a decrease in the number of molecular magnets. The author hopes to continue the investigation and to determine definitely the number and kind of atoms in the elementary magnet, and also to study the effect of the percentage of copper upon the transforma- tion temperature. These results will be important in proving that the magnetic properties are due to the manganese. SUMMARY. The chief results of this investigation may be summarized as follows: 1. The temperature of magnetic transformation from the ferro- magnetic to the paramagnetic state was established at 310 C. for the alloys containing 62 per cent, copper. 2. The curve giving a as a function of the temperature has been shown to agree with the theoretical curve above 200. 3. Chilling from near the melting point causes the experimental curve to follow the theoretical curve to a lower temperature than before. 4. The nature of the molecular field was found to be of the same order of magnitude as nickel, all the constants I m , H m , M and H, being of approximately the same value. 5. The results, while not extensive enough to determine the number and kind of atoms in the elementary magnet, are sufficient to show that the alloys obey the laws of ferro-magnetism, as derived by the present molecular theory. 6. The fundamental equation (i), on which the present theory of No. 4.] THE MAGNETIZATION OF HEUSLER ALLOYS. 305 magnetisms be said, has been derived mathematically; thereby, making the former analogy to the gas theory unnecessary. The writer takes pleasure in acknowledging his indebtedness to Pro- fessor Jakob Kunz for his general supervision of the work, and for many valuable suggestions. LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS, April 25, 1912. [Reprinted from SCIENCE, N. 8., Vol. XXXVL, No. 9S7, Pages 8S7-8S8, December IS, 1912] A SIMPLE DISCHARGE TUBE FOR DEMONSTRATION PURPOSES AT the present time when so much interest is centered on electric discharge phenomena in evacuated tubes it may not be out of place to describe one of the discharge tubes that the writer used recently for class-room demonstra- tion. The experiment is purely qualitative, and in principle contains nothing new. Its aim is to present with simple and easily con- structed apparatus some of the phenomena that are usually given with more elaborate and expensive outfits. It does, however, require that the experimenter have access to, and be familiar with, the operation of an ordinary Geissler mercury pump and an induction coil. Aside from these the things needed are found in almost any laboratory and require no more skill to make than the blowing of a glass Tee. The discharge tube in question is shown in the figure. The bulb may well be a two- or three-liter florence flask. The part to be blown is MN. It supports the aluminum rod carrying at its upper end the spherical or oblong cathode, C, of the same metal. The anode, A., is a cylinder of not too light weight aluminum foil placed in the neck of the flask as shown. Connection to this is made by a fine copper wire led out through the wax joint, RW, at the mouth of the flask. The exhaust tube should contain a glass valve and ter- minate in a sort of ball and socket joint (to be sealed with wax) so that the apparatus may be readily disconnected from the pump. The charcoal bulb, CB, may be dispensed with where liquid air is not available. Liquid air is not a necessity; its use, as is well known, is to hasten the exhaustion. The three joints, RW, may be closed sufficiently air-tight by a good grade of red sealing wax. The various steps, as the exhaustion pro- ceeds, may be vividly shown the stringy dis- charge, the Geissler stage, the formation of striae, the Faraday dark space followed by Crookes dark space, and finally the formation of cathode and X-rays. The phosphorescence due to the latter is strikingly shown by intro- ducing into the bulb a few cubic centimeters of willemite flour (W in the figure). This should be well dusted over the inner surface of the bulb before sealing the apparatus to 8 the pump. A particularly beautiful effect, at the cathode-ray stage, is to disconnect the pump and then shake the bulb vigorously so as to throw the flour through space while the discharge is passing. I" 11 Ill Maximum D.C. || 11 J*s Available Was 1,000 Volts Remarks 2* a s^-2 ^g 2.0 Passed 1.5 freely. More freely. 480 440 Thedischagein each case was Blue at cathode. .5 Still more more volumi- freely. 360 nous than with U = TT. The surface distribution on the infinite plane is obtained by putting x = o in (4) which then becomes * = ',9* ~~^- ( 6 ) WIRE PARALLEL TO Two PLANES INTERSECTING AT RIGHT ANGLES. The equipotential lines and lines of force about a long wire parallel to the intersection of two perpendicular infinite planes are given by the transformation where a = a + bi and = a bi. No. 6,] DETERMINATION OF CAPACITIES. 436 The curves in the z- plane for u equal to a constant are shown in Fig. i. Near the point (a, b) the curves approximate very closely to circles so that the equipotential line C in Fig. i can be replaced by a wire of circular Fig. 1. cross-section without any appreciable error if the radius r is small as compared to the distances a and b. Then the center of this circle can also be taken as the point (a, b). From (7) we have ilog (x* - y - a" + ft 2 ) 2 + 4(*y + ab) 2 (x* - f - a 2 + 6 2 ) 2 + 4(xy - aft) 2 (8) Now since we are considering only the case where r is small as compared to a and b, we can find an expression for the potential at the surface of the wire by placing y = b and x = a r in (8). Then (r- - 2a) (9) Now it can be easily proved that if u in equation (8) represents the potential at the surface of the conductor, the charge on it will be one half unit. Hence the capacity per unit length between the wire and the two planes is i C = U UQ' where UQ is the potential of the two plane conductors. But putting 437 j. w. WOODROW. [VOL. xxxv. xy = o in (8) gives = o, and the capacity becomes I lo V(r - 2 r V( r - 2aY + 4& 2 or, neglecting r as compared to a and &, we have + No. 6.J DETERMINATION OF CAPACITIES. 438 Two WIRES PARALLEL TO THE EARTH AND ONE DIRECTLY ABOVE THE OTHER. It was found that the equipotential lines and the lines of force about two wires parallel to the earth where one is directly above the other could be obtained by the transformation (z 2 + a 2 + ad) - izd = lo *(# + a + 0+r where a is the height of the lower wire and d is the distance between them. This is the case where the lower wire bears a positive charge and the upper wire a negative charge and the radius, r, of the wire is small compared to a and d. Then [x 2 + (y - a - d)*][** + (y + a) 2 ] Z[ x * + (y + a + dnx 2 +(y-a)r The potential u\ of the lower wire is found by putting x = o and y = a-\-r in (16); hence (d - r)*(2a + r) 2 Likewise to obtain the potential of the upper wire, substitute x = o and y = a -\- d -}- r in (16) which then becomes r(2a + d+r)* (2a + 2d Whence the capacity for this system is Y(d - r)(2a + r)(2a + 2d + r)(d + r) 2 log : (19) . /v -h r)(2g + 2J + r) 4l g - r(2a + ^ 4^T Neglecting the second power of r C= =i= . (20) + r)(a + d)+ar] If we take a as infinite, we have simply the case of two parallel wires 439 J - w - WOODROW. [VOL. xxxv. for which the capacity is known to be i C = l + Vp- r* 4 log - r where 2/ is the distance between them. Or neglecting r 2 4 log- 4log- where d is the distance between the wires. Now substituting a equal to infinity in (20) we obtain C = d , (22) 4log- which agrees with the former result. THREE PARALLEL WIRES ARRANGED so AS TO BE AT THE CORNERS OF AN EQUILATERAL TRIANGLE. In transmitting a three-phase alternating current by an overhead system, the wires are generally arranged so that they are at the corners of an equilateral triangle. We shall find the electrostatic capacity of such a system when the total charge on all the wires is zero. There will be no loss of generality if the charge on one of the wires is taken as one positive unit while that on each of the other two is taken as one half a negative unit. Again a very simple transformation can be found which will give the proper lines of force and equipotential. This transformation is . (s 2 - 4<* 2 ) + where the distance between any two wires is 2aV 3. The equipotential lines will be found from the equation 1 . [( - a V3)* + (y + afflfr + a ^3) 2 + (y + a) 2 ] , , = il g " [* + (y - 2a)*p "' (24) which is obtained directly fron (23) in the usual way. In the above the origin has been taken at the intersection of the medians of the triangle and the wire bearing the positive charge has its center at the point (o, 2a), while the other two wires have their centers No. 6.] DETERMINATION OF CAPACITIES. 440 at the points (a V$, a) and (aV$, a) respectively. Hence to find the potential of the first wire we shall place x = o and y = 20, r in (24) as for these small values of r the equipotential lines are approxi- mately circles. Hence we obtain 11 i = \ log - ^- - , (25) (I2 *[( + <) -3*1 [-*(<* + 3*)]' where ^ is the height of the two lower wires above the surface of the earth. Then the expression for the potential is 1} ([**- (y - d}*- 3a , . 1 2 222 -d- 3 a) 2 ] 2 * The potential of the upper wire which bears the positive charge of one unit is found by placing x = o and y = d + 30 r in (31) ; which gives ,. [(3ft ~ r? + 3<* 2 1 2 [2d + 6a - r] < 3* - r) 2 + 3 * 2 ? As before it can be shown that 2 = ~ Ji- (33) 44 1 J- w - WOODROW. [VOL. xxxv. t Hence the capacity of this system becomes (2d + 6a-r) / (3<* - rY 3log r ' \2rf + a -r (34) However for all practical cases r is very small as compared to d so that we may neglect r in (34) wherever it is added to d. This gives [- (35) Placing d equal to infinite in the above equation will give the capacity of the three wires alone. This then is / l/i2a 2 - 6ar + r 2 \ ' 3log(- -7- -) which is the same value found in equation (29). It is also easily seen that the value of the capacity found in (35) is larger than that in (29), as was to be expected. IMAGES IN A CYLINDER. Let us consider the transformation R 2 az . . "-^ (37) This gives for u __ V(ff - axY + a*y* . ...; " = log RV (x - a ?^- ; (38) For u = o, we have (R* - ax)* + aV = 2 [(* - a) 2 + /], whence x z + y z = R 2 . (39) That is, the zero potential surface is a cylinder and the cross-section in the :ry-plane is a circle of radius R. Again from equation (38), we obtain (R* - axY + oV e " ~ - a) No. 6.] and or DETERMINATION OF CAPACITIES. 442 y z - aR 2 - /l2 - 2 = o, / (* ~ a 2 - 2 )1 2 TT-? 2 J (40 Hence the equipotential lines are all circles with their centers on the #-axis and at a distance from the origin given by The radii are given by e 2 - i R 2 e 2 -a 2 ' eR(a 2 - R 2 ) R 2 e 2 " - a 2 ' (42) in which the positive sign is to be used for values of u greater than u = log (air) and the negative sign for values less than that. The Fig. 2. reason for this is quite obvious from Fig. 2. The radius becomes infinite for u log (a/r) and the equipotential curve becomes the straight line x = 20, Now let r\ be the radius of a small wire bearing a charge of one half unit per unit length placed parallel to a large, earthed, cylindrical conduc- tor of radius R and let d be the distance between the centers of the two. Then we can replace the cylinder by another wire bearing a negative charge of one half unit without any change in the electrostatic field. To find the radius r* and the position of this latter wire replace u by u in equations (41) and (42). It will be seen that r 2 is less than r\ as might 443 J - w - WOOD ROW. [VOL. xxxv. be expected. For e u R(a 2 - R 2 ) e u R(a 2 - R 2 ) ri ~ R 2 e 2u -a 2 ' r *~ a 2 e 2u - R 2 * Also the positions of the centers of the wires will be given by '' (44) It is to be understood that the above reasoning only holds for the case where very long and large cylinders are considered. It can readily be shown that the method of images does not apply rigorously to the case of two long small parallel wires at any considerable distance. That is, as suggested earlier in this paper, the electric force in the direction of the 2-axis must be so small that it may be neglected. However in this as in the general theory of the logarithmic potential, the very long wires must be considered as finite in length when applying the test of zero potential at an infinite distance. Now equation (38) may be used for finding the capacity between a wire bearing a charge and an earthed wire near it. First consider the case where the small wire is external to the earthed cylinder. The first of equations (43) gives a z - R 2 ) (46) l ~ R 2 e 2u - a 2 from which we find R 2 (eR From the first of equations (45) * whence 2 = ( 1 = e u Solving for e u , \(t\ Y\ J\. ) | \v~i . j. " / T^- ' A /. \ e = -^ ~ , (47) and Now it is easily proved that the charge on the wire is one half a unit, so that the capacity of this system is No. 6.] DETERMINATION OF CAPACITIES. 444 (dt - ri 2 - R 2 ) 2log - Likewise the capacity between the internal wire and the cylinder may be found from the second of the equations (44) and (45) respectively. This gives (S* + rt - df) 2log " To prove that the above expressions have the proper form, place d = i + R and let R become infinite; that is, let the earthed cylinder become an infinite earthed plane. This gives l + Vl 2 -r 2 2 log - j- which is the identical expression previously obtained for a wire parallel to an infinite earthed plane. An expression for the surface distribution over the earthed cylinder is very easily obtained. From equation (37) we obtain dw R 2 - a 2 dz az 2 - z(R 2 + a 2 ) + aR 2 ' Taking the absolute value and simplifying R 2 -a 2 dw dz V[a(x 2 -y 2 + R 2 ) - x(R 2 + a 2 )] 2 + \y(2ax - R 2 - a 2 } 2 Transforming to polar coordinates dw R 2 a 2 dz ~ R(R 2 -r- a 2 - 2aR cos ) and a can be calculated for any particular system from equation (46). It is seen that the maximum value of a is for = o and the minimum value for

Then placing a = R/3, we have (R - r)(^R - r) r(5R - r) And the capacity between the two wires within the earthed sheath is i (R - r)(4* - r) ' 4l g - r( 5 R-r) (58) It is to be understood that this latter form is an approximation that can be used only for small wires so placed that the distance from the surface of one wire to the surface of the other is equal to the distance from the inner surface of the metal sheath to the surface of the nearest wire. However the method can be adapted to other conditions by taking the proper relations between a, r, and R. THREE CORE CABLES. A transformation was found which would give equipotential lines which very nearly coincide with those in the clove-leaf type of three-core cable. A diagram of this cable is shown in Russell's Alternating Currents, Vol. I. This transformation is ((z* - R*) + Rzi] - (z - log 2 _ . _ > ' where the distance between the surfaces of the bundles of wires is equal to the distance from the inner surface of the enclosing metal sheath to the surface of one bundle of wires. The charge on one of the con- ductors is one positive unit, while each of the other two has a negative charge of one half unit. Then the equation of an equipotential line becomes , 1 ,, , g ** 22 ** zz2 ' ( } [x z +(y-R) z ] 2 Now if d is the distance from the center of the circular cylinder to the No. 6.] DETERMINATION OF CAPACITIES. 448 outer surfaces of the bundles of wires, an expression for the potential of the wire bearing the positive charge will be obtained by substituting x = o and y = d in (60). This gives HI = log - d)V / (R + d) 2 - Rd 1 (61) Now it can be proved that the potential of the conductors bearing the negative charge is Hence the capacity of the system is / T" 7 [ / T" 1 7\ O T- T \ \ J / 4R 8 \R- 4R- d (R + d)* - Rd R - d X UR + d) 2 - 3 If the conductors are small wires of circular cross-section, and radius r, a close approximation to the value of the capacity will be obtained by substituting d = %R + r in (62). For this condition then C = - (63) , log /7*-2r 7^ + 8^ + 4^ 5 V 2R - 4 r ' \f iSR* + $Rr + r*l It may seem at first that too many approximations have been made in this paper, but a closer examination will show that the results obtained by using the formulae derived will, for nearly all practical cases, be more accurate than the measurements from which the calculations are made. In the cases of the cables if the wires have the shape of the equipotential lines, the results will be exact. In conclusion I wish to thank Dr. J. Kunz and Professor E. J. Townend for their many helpful suggestions during the investigation of the above problems. LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS, August, 1912. Reprinted from School Science and Mathematics, Vol. 13, 1913. Pages 421-422. THE PROJECTION OF "THE GUINEA AND THE FEATHER" EXPERIMENT. BY A. P. CARMAN., ^ University of Illinois. The usual apparatus for "the guinea and the feather" experi- ment, to show all that all bodies fall with the same acceleration in a vacuum, consists of a glass tube three or four inches in diameter, with a eoih and a feather inside. Upon inverting the exhausted tube quickly, those near by can see that the two objects fall some- what together. The objects however often strike the sides of the tube, and the observation is that the two objects "would" fall to- gether if they fell freely. For a large class, the experiment is also unsatisfactory because most of the class see nothing. The experiment is so important in explaining "weight" and "mass/' and has such historical importance that the writer and his as- sistants arranged apparatus so that the two objects are released at the same instant and fall freely, and so that a large class can see the occurrence by the direct shadow method of projection. The arrangements simple, but it has been suggestive and useful to some who have seen it, and so it is described here. 422 SCHOOL SCIENCE AND MATHEMATICS An air-tight rectangular box of metal and glass was made, (Figure) forty inches long and with cross-section six inches square. The section could just as well be reduced to four inches square. The top, bottom and two of the opposite sides are of cast iron, the other two sides are of heavy plate glass cemented to the planed iron surfaces, and in addition held in place by clamps. A hose connection with stop-cock C is placed in one side for ex- hausting the air. There is a three inch circular opening in the top, and this is closed by a plane metal plate M, the fit of which is made air-tight by a flat rubber ring. Through this plate, there are insulated electrical binding posts and connectors, .which carry on the under side a loop of small fuse wire. On this fuse wire are hung a feather F and a bullet B. These are released ai the same instant by melting the fuse wire with an electric current. The box is placed in the light of the projection lantern, so that the shadows of the feather and bullet are distinct on the screen. When the objects are released by making the electric circuit, they fall, so far as the eye can tell, absolutely together, if the box is exhausted. The simultaneous fall can be seen clearly by every- one in the lecture room. An additional advantage of this ap- paratus is that it is separate from the air pump and is always ready. Reprinted from School Science and Mathematics, Vol. 13, 1913. Pages 1-9. SOME RECENT PHYSICAL THEORY.i BY ALBERT P. CARMAN, University of Illinois. The announcement by Wilhelm von Rontgen in December, 1895, of his discovery of a new kind of radiation, created an immediate and widespread interest which has probably not been exceeded in the history of science. But the importance of that event was far greater than the announcement of a striking and astonishing discovery. The subsequent developments of physics and chemistry show that Rontgen's discovery marks the practical beginning of a new era in physical science. While our knowl- edge of the nature of X-rays has increased little beyond what we learned in the first few months after their discovery, the investi- gations started and suggested by Rontgen's discovery have revolutionized our concepts and theories in nearly every field of physics. Thus Sir J. J. Thomson was started with a new im- pulse into the investigations of the nature of the cathode rays and the mechanism of the electrical conductivity of gases, and these investigations led directly to the discovery of the cor- puscle or electron. In France, Becquerel was inspired to study the fluorescent effects of many minerals, and the next year after Rontgen's announcement came the epoch making discovery of the Becquerel rays, a phenomenon which might have remained unknown for another generation, had it not been for the sug- gestion of the Rontgen rays. Following this lead, we have the great investigations of the Curies, Rutherford, Ramsey, and many others in the subject of radioactivity and of the nature of the chemical elements. The concepts thus introduced and the methods made possible by the new phenomena, have enabled physicists and chemists to re-open old investigations, and the facts thus revealed have given us new interpretations of many old results that were thought complete. We are still in the midst of this scientific era, and much remains speculative and unsettled, yet it has seemed well to spend a short time in discuss- iRead at the meetinp of the Central Association of Science and Mathematics held with Northwestern University, Evanston, 111., Nov. 29, 1912. 2 SCHOOL SCIENCE AND MATHEMATICS ing some of the newer concepts which must affect our beginning statements and definitions, and hence must interest us most vitally as students and teachers of physics. Perhaps no concept ever dominated science so completely as did the concept of the aether dominate physics during the nine- teenth century. The aether was the medium of which eminent thinkers and writers told us that we knew more about than we do about air or any other form of matter. By this medium we explained the action and nature of light, the transmission of electrical and magnetic induction, and even of gravitational force. Matter itself was supposed to be whirls or vortices in this aether, and positive and negative electricity were simply boundary conditions due to the displacements of the aether. Many of the greatest minds of the nineteenth century spent their best energies in the development of a physics of the aether. Such intellectual giants as Fresnel, Kelvin, Maxwell, Stokes, Mac- Cullough, Helmholtz, Hertz and Poincare worked at the prob- lems of this universal medium which was thus to advance us further in solving the mystery of the universe. The aether was primarily a concept to explain the propagation of such periodic disturbances as visible and invisible light. The concept of a luminous aether was first stated in a tangible form by Christian Huygens and Robert Hooke in the seventeenth century, but it was not until the very beginning of the nineteenth century that it displaced the corpuscular or emission theory which we ascribe, perhaps improperly, to Sir Isaac Newton. Then came the bril- liant discoveries of the interference of light by Dr. Thomas Young in England, and Augustin Fresnel in France, with their direct explanation on the undulatory aether hypothesis. This was followed by Fresnel's work in the polarization and double refraction of light, so that before Fresnel's death in 1827, there were few who questioned the undulatory theory of light and the existence of a luminous aether. But there were difficulties in the concept, and it called for all the skill of Kelvin and other great mathematical physicists of the middle of the last century to develop the so-called "elastic solid theory" of the aether, which should meet the facts of with even approximate satisfaction. During these same years, Michael Faraday had been develop- ing his theory of electric and magnetic fields, and had given to science his great concept of lines of electric force. Faraday did not at first assume any medium for the lines of force, and even as late as 1851, he seems to have had his doubts about the RECENT PHYSICAL THEORY 3 necessity of an aether for the transmission of electrical and magnetic forces across space. While he suggested that the luminous aether might ''have other uses than simply the convey- ^ance of radiation," and might be the vehicle of magnetic force, it was not Faraday, but James Clerk Maxwell, who developed the concept of the electromagnetic luminous aether. Maxwell took up the problem which was placed before him by Faraday's "Ex- perimental Researches in Electricity." He was equipped for the work by his training in the University of Cambridge which has for centuries been one of the world's great mathematical centers and he developed a theory which has been the admira- tion of both physicists and mathematicians. Maxwell's electro- magnetic theory identified electrical and magnetic phenomena as disturbances in the same medium as light, and indeed made light an electromagnetic wave in the aether. This theory gained recognition slowly, but after 1887 and 1888, when Heinrich Hertz demonstrated by his brilliant experiments the existence and properties of electric waves, there seemed to be nothing more firmly fixed in physics than the existence of an electromag- netic luminous aether. Thus Sir Oliver Lodge in his book on Modern Views of Electricity, edition of 1899, describes the aether as "one continuous substance filling all space ; which can vibrate as light ; which can be sheared into positive and negative electricity ; which in whirls constitutes matter; and which transmits by con- tinuity and not by impact every action and reaction of which mat- ter is capable." A theory which was so dominant with the most ad- vanced and profound thinkers in physical science, naturally came to be the view presented in the manuals of physics, so that we find the aether concept of electricity and light was the view presented in our most progressive elementary text-books of scarcely a decade ago. But while these elaborate and extensive theories of the aether were held generally, there were some thinkers who felt that the experimental foundations were neither broad nor sure enough for such a big structure of theory. Thus Lord Salisbury, in the Pres- idential address before th,e British Association for the Advance- ment of Science in 1894, describes the aether as simply the subject of the verb "to undulate." That is, he calls attention to the fact that the aether is a concept to explain the transmission of light waves, and that is all we really know about it. The rest is speculation. One of the greatest difficulties of the aether theory, was the 4 SCHOOL SCIENCE AND MATHEMATICS explanation of the nature of the electric charge as it appears in electrolysis. The explanation of the electric current through metallic conductors in the Maxwell theory, was certainly not simple, though it gave a possible solution, but the passage of electricity through an electrolyte was confessedly incomplete. Much more incomplete was the theory of electric discharge across gases. These phenomena, we are told, greatly interested Max- well, but the whole subject of discharge through gases occupies but a few short sections in his great "Treatise on Electricity and Magnetism." While Faraday, Pliicker and others had fixed some of the fundamental facts of discharge in vacuum tubes, yet at the time of the publication of Maxwell's treatise in 1873, the facts known were too fragmentary and indefinite to form the basis for any general theory. At the time of Rontgen's dis- covery, there had sprung up a renewed activity in the investiga- tion of the phenomena of electric discharges in exhausted tubes. Lenard had discovered rays that penetrated aluminum windows in the tube, and J. J. Thomson had already begun his epoch making investigations in this field. Rontgen's startling discov- ery gave the new impulse to Thomson's work and this resulted in the atomic or electron ^ theory of electricity. The electron theories that followed have completely displaced the aether theories for many phenomena. Thus the electric charge is no longer re- garded as a shear of the aether, but as a collection of electrons ; the electric current in a wire becomes a flow of electrons, and not a breaking down of the aether strains along the metallic wire ; an elementary or molecular magnet is no longer due to aether whirls, but is due to the rotation of one or more electrons about the material atom. The asther vortex theory of matter of Kelvin and Helmholtz has been replaced by the corpuscular theory of matter of J. J. Thomson. The inertia of matter, thus becomes the electromagnetic inertia of the moving electrons of which all matter is built up. Within a little over a decade, the corpus- cular theory developed by Thomson and his school displaced a large part of the physics of the electric aether which the men of the 19th century built up with such great labor. The investiga- tions by Rutherford and the Curies in radioactivity contributed largely to this revolution of our concepts. Rutherford showed that radium gave off three types of rays, and that two of them, the a and /? rays, are corpuscular or atomic in nature. The third type of rays, the y rays, it has been commonly thought are the same as the X-rays of Rontgen, and these have been RECENT PHYSICAL THEORY 5 thought of as pulses of the aether produced by impacts of elec- trons. But even here, there has arisen a question of the necessity of sether, for a brilliant experimenter Professor Bragg of Leeds, believes that he has shown that the y rays are corpuscular or atomic. If the y rays are corpuscular, then Bragg's conclusion is that X-rays are corpuscular and not aether pulses. This starts another question, for the X-rays and the ultra violet light show many similar properties and so we are led to ask, is not ultra violet light corpuscular as well as the X-rays? And if ultra violet light is corpuscular, why is not all light and radiation to be con- sidered as corpuscular. Bragg's concept of the y rays is that they are doublets of positive and negative corpuscles, so that the periodic character of such a radiation might come easily as a con- sequence of the vibration of the advancing doublets. If this bold speculation prove to be true, we shall be back to a Newtonian cor- puscular theory of light, and the concept of an aether would be rendered still more unnecessary. But how explain the existence of lines of electric and magnetic force in a vacuum? The aether theory said, "they are made of the aether, the medium which fills all space and through which light is propagated that is, they are the lines of strain- and stress in the intervening medium." The newer school seem to have gone back to Faraday's very first tentative ideas of lines of force, and to give these lines an objective existence independent of any medium. Thus Mr. Norman Campbell in his recent book, entitled "The Principles of Electricity," says : "Lines of force are just lines of force independent for their existence of all surrounding bodies, and there is no more to be said about them. If lines of force passing through sulphur are not made of sulphur, there is no need, when the lines pass through a vacuum to imagine the vacuum filled with a substance of which the lines may be made; in other words, our electrical theory, so far from providing additional support for the conception of the aether filling all space, does not require such a conception at all. All it needs is the conception of lines of force ; where there are no lines there is no need for the presence of anything at all. We do not require to imagine present everywhere a substance of which the lines of force may be made when charged bodies come into the neighborhood, for the bodies bring their own lines with them, ready made and unalterable." He says further in emphasis, "The idea that an aether existing everywhere is needed for Fara- day's theory is not necessary; all that is necessary are the lines 6 SCHOOL SCIENCE AND MATHEMATICS of force, which are not made of the medium through which they pass." Mr. Campbell, whom we are thus quoting represents views which are more radical in details than some physicists agree to, but certain it is, that the electrical and magnetic aether, even if we call intervening space by that name, is an entirely different conception from that held so generally a dozen years ago or less, and which still persists in text-books. We turn now to an entirely different line of inquiry that is the investigation of the radiation from a black body. When a blackened body, such as a carbon filament, is raised in tempera- ture, it gives off radiant energy which increases in amount and also in frequency as the temperature rises. The law of radiation from an ideal "black body," that is, from a body which radiates and absorbs perfectly, has been studied by many physicists and numbers of theoretical formulae have been proposed. About 1895, a group of German physicists, prominent among whom were Professors Lummer, Pringsheim and Kiirlbaum of Berlin, began to give us exact experimental results on the radiation and the temperature in the case of a uniformly heated cavity which was nearly closed, and which for all practical purposes realized Kirchhoff's ideal black body. These and later results have afforded a guide and test to the theoretical radiation formulas of Wien, Rayleigh, Jeans, Planck, Kunz and others. Of these formulas, that of Planck has been most widely accepted, though the firmness of its theory has been questioned and some think the agreement with experiment to be accidental and apparent and not real. Planck started with the concept of the electro- magnetic origin of radiant energy. He assumes it due to vibrat- ing electrons in the atom and takes Hertz electric oscillator as the type of the electronic oscillator. This is the common type familiar to students of electric waves and simple wireless teleg- raphy. As stated the formula thus derived agrees fairly well with our present experimental results for a wide range of tem- peratiures and hence has received wide acceptance. The most striking fact of Planck's radiation theory is, however, that it leads to Planck's "quantum" or atomic hypothesis of radiant energy. This hypothesis says that radiant energy is not to be considered as infinitely divisible and continuous, but as discrete and made up of a great number of finite and probably equal parts, called by Planck, "quanta." Professor Einstein of Zurich, who is one of the first of living mathematical physicists, has gone beyond Planck's conception, and says that a ray of light consists of RECENT PHYSICAL THEORY 7 innumerable atoms of energy or light quanta, that is, that the light exists in space in discreet light atoms, or quanta, and is not con- tinuous as the aether wave theory assumes. It is not possible in a short paper to present the detailed rea- sons which have led Planck, Einstein and others to these new views of the nature of radiant energy. The papers of Planck, Einstein, Sommerfeld, Nernst and others must be studied by one who wishes to understand how firm a hold this atomic theory of radiant energy and light has upon a large group of the most profound thinkers in physical science today. Certainly if we are to accept an atomic theory of electricity and an electronic theory of matter, then there is nothing strange or absurd in an atomic or corpuscular theory of the light and radiation coming from matter, for Zeeman, Lorentz and others have shown the close connection between the vibrating electron and the emitted light. It would however sound strange to Helmholtz and the physicists of his generation to learn that we have come back to a theory so closely resembling the Newtonian emission theory. We thus see that the electron theories are leading us to ideas of discrete quantities of not only electric but also light energy. This is manifestly not in accord with th,e concept of a continuous aether. One of the fundamental questions about the aether has always been, is the aether stationary or does it move with the earth? The experiments on this question are so contradictory that a whole group of leading scientific men have been led to deny not only the existence of the asth,er, but also to revise the "common sense" ideas of time and space which have always been used by physicists, whatever their metaphysical creed might be. On one hand we have the famous aberration observations of James Bradley made in 1728, that a ray of light from a star appears to come at a slanting angle. This is explained directly as due to the composition of the velocities of the earth and of the light. Thus if the light is a disturbance in the aether, the aether must be stationary in reference to the earth. On the other hand, we have the recent experiments of Michelson and Morley and Miller, of Brace, and of others, which show that the apparent velocity of a ray of light does not depend upon whether the direction of the light is the same as that of the earth or not. The direct inter- pretation of these last experiments is that there is no relative motion of the aether and of the earth. It is probable that these experiments on aether drift have been with most physicists the greatest reason for questioning the aether concept of luminous 8 SCHOOL SCIENCE AND MATHEMATICS transmission. Thus Fitzgerald and Lorentz have suggested a possible explanation in assuming that material bodies shrink in the direction of the aether drift, and hence the change in the light velocity would be hidden. This is however giving us a meter bar of shifting length, and most of us like to think of something as fixed. A recent writer says, "Almost any experi- mental result can be reconciled with almost any theory if sufficient subsidiary assumptions are made ; the only question is whether it is worth making them." As said above, many do not think the original concept is worth making the necessary subsidiary as- sumptions. The question involved in a stationary or moving aether is a very big one, and it is mentioned here simply as another evidence of the drift away from the aether concept, in its old form at least. From what we have been saying it will be seen that there is at present a decided tendency in physics to go back to the older separate entities and to abandon the continuous fluid ideas as- sociated with the aether concept. Thus we have the electron instead of Maxwell's aether "displacement" and if Planck's radia- tion theory is to be accepted, we have a corpuscular concep- tion of energy. An interesting extension of this same idea, is given in Professor Callendar's address before the Physics Sec- tion of the B. A. A. S. in its meeting at Aberdeen last August. Professor Callendar suggests that recent discoveries point to- wards a material theory of heat, and he then proceeds to show that a modified caloric theory of heat affords reasonable ex- planations of thermal phenomena. He further advances the spec- ulation that this caloric may be neutral corpuscles. That the countrymen and students of Kelvin, Joule, Tait, Rankine and Tyndal should entertain with scientific seriousness the discussion of a corpuscular theory of heat by one of their leading physicists, is indeed very significant. If, however, an atomic or quanta theory of radiant energy is to be accepted," it is certainly not many steps to a caloric theory of heat. It is thus evident that we are in a period of new fundamental theories in physics. To the student of physics it is a most inter- esting and stimulating time, with opportunities and invitations for telling work in nearly every field of physics. To the teacher who is stating and presenting the elements of the subject, the situation is not simple. To keep abreast of the advances in fundamental concepts, and still keep on safe ground is not easy. Further, the theory that appears simplest to present may not be R EC EXT PHYSICAL THEORY that which is nearest the truth. Thus Professor Callendar sug- gests that the kinetic theory of heat has come to. be adopted to the exclusion of the material idea, because, quoting his words, "The kinetic theory is generally preferable for elementary ex- position." In this .particular case most of us are not yet ready to abandon" the essentials of a kinetic theory of heat, but the idea suggested of giving a theory because it. is "preferable for elementary exposition" raises a question. There are indeed those who hold that a theory is simply scaffolding and not a serious attempt to build a permanent structure. There is a system of philosophy which claims to be copying the methods of natural science which confesses that its explanations are purely specula- tive and cares nothing for reality. Indeed it is claimed that the number of possible working theories of material phenomena is indefinite and that the theory that we adopt is simply a question of convenience in thinking. The general introduction of such metaphysical ideas into physics would be fatal to advance. As students and teachers of physics, we must believe and teach that a physical theory is a real explanation of real phenomena, if the physics of this century is to equal and excel the triumphs of the physics of the last century. Determination theorique de la variation de la masse de 1' electron en fonction de la vitesse JACOB KUNZ ABSTRACT Archives des sciences physiques et naturelles de Geneve, tome XXXV, 1913, p. 28. It is assumed in this article that the electromagnetic field surrounding a moving electron is endowed with mass, momentum and energy. The expression for the mass per unit volume as suggested by the pressure of light, is uk 2 E 2 sin 2 ' ( > m i = 4 7T The resultant electromagnetic mass depends on the shape of the electron. If we assume that the electron during the motion remains spherical we obtain for the mass: If the electron contracts according to the law we find m_ i m o V 1 v ^_ (2) c 2 the formula given by relativity for the transversal mass of the electron. If the electron contracts according to the law a c^ the integration yields the result HL_3 o c 2 -v* /_g_ 3\ i+i 3 Ml _cVJ (3) m.~8 v v 2 \c 2 v 2 4/ 8 i -^ i6(c 2 v 2 )v 2 C It is shown that the first formula gives values 1 3% smaller than the experimental values ; the second formula, that of relativity, agrees very well with the facts ; the third formula gives too large values. THE VELOCITY OF ELECTRONS IN THE PHOTO-ELECTRIC EFFECT, AS A FUNCTION OF THE WAVE LENGTHS OF THE LIGHT BY DAVID W. CORNELIUS (Reprinted from the PHYSICAL REVIEW, N.S., Vol. I., No. i, Jan., 1913.] THE VELOCITY OF ELECTRONS IN THE PHOTO-ELECTRIC EFFECT, AS A FUNCTION OF THE WAVE LENGTHS OF THE LIGHT. BY DAVID W. CORNELIUS. THE object of this investigation is a determination of the potential acquired by alkali metals when illuminated by light of different wave-lengths, and the determination of the velocity of the electrons as a function of the frequency of the incident light. Besides the direct interest of these measurements, the importance of this investigation lies in its connection with the general theory of radiation of the black body as developed by Planck by means of the calculus of probability and thermodynamics. In Planck's theory, which has been well confirmed by the experiments on the radiation of the black body, which also gives ^ood values for the elementary quantities of nature, the elementary oscillator emits the radiant energy not continuously, but intermittently in definite units such that the elementary unit of radiation energy is pro- portional to the frequency of the light. The equation is E = hn, where E is the energy, n is the frequency and h is a constant of pro- portionality. On this theory we should expect the positive potential of the photo-electric effect to increase proportionally to n. Some of the first determinations of the velocities of electrons emitted from alkali metals under the action of light of different wave-lengths have been made by Jakob Kunz, 1 who found that the potentials are nearly proportional to the square of the frequencies of the incident light, and that the veloci- ties are almost independent of the temperature and of the intensity of the light. Two other recent papers make further measurements im- portant. J. R. Wright 2 finds that there is a decided maximum in the curve representing potential and frequency in the case of zinc; and R. Pohl and P. Pringsheim 3 find that there are two different photo-electric effects in the alkali metals, the ordinary and the selective effect. They measured, however, the photo-electric currents, and not the equilibrium 1 J. Kunz, PHYS. REV., Vol. 29, 3, 1909; Vol. 31, 5, 1910. 2 J. R. Wright, PHYS. REV., Vol. 33, i, 1911. 8 R. Pohl and P. Pringsheim, Verhandlungen, d. D. Phys. Gesellschaft, 12, p. 215, 1910; and R. Pohl, Verhandlungen, d. D. Phys. Gesellschaft, n, 715, 1909; 13, 961, 1911. VOL. I.I No. i. J VELOCITY. OF ELECTRONS. potential acquired by the metals. It is therefore important to ascertain whether there are two different effects to be found in this equilibrium potential, whether there is a maximum, or whether the potential increases continuously throughout the range of the visible light. Finally the influence of the temperature on the equilibrium potential has to be determined. DESCRIPTION OF APPARATUS AND METHOD. The arrangement of the essential parts of the apparatus used in this research is shown in Figs. I and 2. The source of light is a carbon arc L. Fig. 1. The light passes through a slit and system of lenses which gives a beam of parallel light upon the prism P, which is capable of rotation, thus providing for an intense source of light, which after passing through the prism, falls upon the slit S of a light-tight box containing the photo- electric cell. By rotating the prism P any desired wave-length can be made to pass through the slit S and fall upon the photo-electric metal C. The illuminated electrode C of the cell is connected through a key K and commutator R to a pair of *"irr,r quadrants of a Dolazalek electrometer E. Static pj g 2. charges were avoided by having the cell, connections, keys and measuring instrument, which were manipulated from a distance, all inside of earthed conductors. The insulators were made of sulphur and amber plugs. The light which passes through the slit S falls upon the metal in the photo-electric cell . The mirror m is mounted so that it can be rotated about the axis ab. The light of the same wave-length as is incident upon the metal is therefore incident upon the mirror. The light is reflected from the mirror into a direct reading spectrometer H, made by Hilger, which was calibrated by means of the sodium lines. This proved to be a very satisfactory arrangement, since the readings of wave-length could be made as the rotating prism was rotated into a 1 8 DAVID W. CORNELIUS. desired position. The suspension of the electrometer was a fine quartz fiber which was made conducting by CaCl 2 for a portion of the work, and a fine phosphor bronze wire for the remainder. The deflection of the electrometer was read by the image of an incandescent light focused on a millimeter scale at a distance of about five meters from the mirror of the electrometer needle. The electrometer was calibrated by means of a standard Weston cell, resistances and storage battery in the usual way. The calibration of the electrometer is practically a straight line. That is, the deflections were proportional to voltage. The sensibility was .00 1 1 volt per mm. deflection. The electrometer was calibrated several times with practically the same results. The maximum potential acquired by the metal, for incident light of any given wave-length, was determined by the deflection of the electrometer. Various voltages were used on the needle ranging from 40 to 140, depending upon the sensibility desired. A number of photo-electric cells were constructed, containing different metals. The designs of the cells varied considerably. The determina- tion of the velocity of electrons emitted from the surface of a photo- electric metal in a vacuum tube, when acted upon by light, was attempted by different methods. The stream of negatively charged electrons will be deflected if it passes through a magnetic field. The velocity of the electrons can be calculated by the ratio e/m, where e is the charge and m the mass of the electron, along with H, the magnetic field and the deflec- tion of the stream of electrons. The magnetic deflection method was tried in several tubes. The advantage of this method is that it gives an independent determination of the velocity of the electrons, so that it would be desirable to be able to use it. After repeated trials the magnetic deflection method was given up, since it was found impossible to measure the photo-electric current. The method of measuring the equilibrium potential by means of an electrometer is subject to certain objections which could not be made against the deflection method. Any conduc- tivity along the glass wall or through the vapor of the alkali metal diminishes the final value of the equilibrium potential. Moreover the potential measured by the electrometer is due to the equilibrium potential and partly to contact electro-motive forces or potential differences of any other nature. All those influences could at once be avoided by the magnetic deflection method. Several cells, which are not shown in a diagram, were unsuccessful. Two rubidium cells showed some interesting features. Exposed to light they showed in the beginning considerable sensitiveness, which decayed rapidly until they did not respond even to intense light. After being left NS"i!'] VELOCITY OF ELECTRONS. 19 in the dark for a short time, they would sometimes recover. The photo- electric metal was melted several times, but apparently was not effective in changing the behavior of the cells. The same behavior was observed in a potassium cell. It was put in sunlight for several hours, but this did not result in the cell becoming consistently active. This phenomenon might be called a fatigue, the cause and character of it are still uncertain. Thus we see that this work is attended with many difficulties. There are a number of sources of error. A small leak in the tube, a slight impurity of the photo-electric metal, and its surface conditions, gas developed in the tube due to wax joints or occluded gas in the metals in the tube, static charges on the glass of the tube, imperfect insulation between the electrodes of the cell, enter as factors, rendering this experimental work difficult of execution. In several experiments it has been observed that the photo-electric metal in the dark chamber acquired spontaneously a negative potential, which developed very slowly and arose to quite considerable values. This effect has since been studied by J. W. Wood- Fig. 3. Fig. 4. row. In those cells which gave the best and most consistent results this negative effect has not been observed. If it existed it must have been so slow that it could not effect the readings to any measurable amount. The general type of cell which has proved to be the most satisfactory in this investigation is shown in Figs. 3 and 4. The metals used were potassium, potassium "fixed" with hydrogen, caesium, and caesium "fixed" with hydrogen. There were only slight variations of the design of the cell to suit the introduction of the different metals, or conditions desired for the cell. Csesium was prepared for introduction into the cell, by first drying caesium chloride by melting it in contact with dry hydrochloric acid gas. Fourteen grams of dry caesium chloride were mixed with 2.5 grams calcium, placed in an iron boat in a combustion tube of Bohemian glass. When the temperature rises the reaction beween the Ca and the CsCl, or RbCl, becomes quite violent and the calcium and the salts spread out and condense together with the rubidium, or caesium, in the cooler parts of the combustion tube. To prevent this mixture, a plug of 2O DAVID W. CORNELIUS. asbestos and iron wire keep the iron boat in position and allow the rubidium, or caesium, vapor alone to pass through the plug. The com- bustion tube is connected by means of sealing wax and glass tubes to the photo-electric cell. After the tube was exhausted the combustion tube was heated gradually until the metal distilled and ran through the connecting tubes into the cell. Rubidium and caesium were both pre- pared in the same manner. Potassium was introduced into the bulb M, of Figs. 3 and 4, distilled into K and poured into C. The cells were all exhausted by a Gaede pump. The vacuum in each case was tested by the characteristics of the discharge, from an induction coil between two electrodes in the system. A flame was kept under the charcoal bulb for several hours until the charcoal ceased to develop gas and the pump was able to exhaust the system to a stage of hard Roentgen rays. If the metal introduced was to be left in the pure state without hydrogen, the tube was sealed off from the pump as soon as the metal was distilled and transferred into the final position. However, if ihe metal was to be "fixed" with the hydrogen, the cell was not sealed T)ff from the pump until later. The hydrogen was introduced by means of palladium, Pd, of Figs. 3 and 4. This metal was used as a cathode in a solution of three parts water, and one part H 2 SO 4 When the electric current passes through this cell the Pd absorbs a large amount of hydrogen which is given off again by gently heating the dry metal with a bunsen flame, in Pd of Figs. 3 and 4. When the cell contains a small amount of hydrogen and a discharge passes from the alkali metal to the anode the surface of the alkali metal assumes very intense colors, due to the com- bination of the metal with hydrogen or else to a colloidal transformation of the metal. This process we may call fixing or forming. In this forming the potassium assumes intense blue or purple colors, while the caesium ex- hibits a greenish gray or bronze surface. A caesium cell No. 10 without charcoal bulb is shown in Fig. 5. Caesium is distilled into the bulb at C when the electrode A is raised, by means of a p. - magnet, in order that no caesium vapor condense upon the electrode. The diameter of the bulb is about 5 cm., and the distance between A and C about 2 cm. The data for this cell are given in Table I. The curve of Table I. is quite similar to that obtained by Jakob Kunz 1 under similar circumstances. The cells which he used did not have any charcoal bulbs attached. Thus it will be noted that this cell which does *J. Kunz, PHYS. REV., Vol. 29, 3, 1909. VOL. I. No. i. VELOCITY OF ELECTRONS. not have charcoal bulb attached verifies his work. The variations of this curve from a smooth curve is in a measure due to residual pressure in the cell. This error is reduced almost entirely where charcoal and liquid air are used. TABLE I. Cesium Cell No. 10. t = 23 C. Wave-length. X MM Frequency 2 . JV* I0*> Volts. V Wave-length. MM Frequency 2 . TV 2 I0*> Volts. V. 420 .510 1.168 570 .278 0.606 450 .444 1.090 600 .250 0.517 480 .391 1.010 630 .227 0.387 510 .346 0.920 660 .207 0.343 540 .309 0.748 690 .189 0.325 Volts on needle of electrometer 126. = .001202. Caesium cell No. 12 was similar to Fig. 3. The metal was distilled upon an iron plate at B of Fig. 3 and moved by means of a magnet to a final position C. A is an alu- minium plate 1X3 cm. The distance between electrodes was about 4 mm. The tube was 2 cm. in diameter and 18 cm. long. The caesium was not "fixed " with hydrogen before the cell was sealed from the pump, The cell was first tried with the 03 02 0.1 a JH WVL LENGTHS 42. 4<> Fig. 6. metal pure, but was found not to- be photo-electric. After three days' effort it was decided to "fix" the metal. It was done in the usual manner. However, since the cell had been previously sealed from the pump, the residual hydro- gen in the tube was not pumped out after fixing, but left for the char- coal to absorb when immersed in liquid air. The results of this cell are given in Fig. 6. Liquid air was kept on the charcoal bulb continuously during the series of observations. The time elapsing between the read- ings for curves 1-4 was about 43 hours. The characteristics of the curves change gradually with time. This is due probably to the absorption of the residual hydrogen, by the charcoal. The change seems to indicate that the curves are approaching a form such as would finally make the maximum potential proportional to the square of the frequency. It was impossible to keep liquid air on the cell 22 DAVID W. CORNELIUS. [SECOND [SERIES. continuously, and make observations until such a steady state was reached. It is probable, moreover, that the surface of the metal under- goes slight changes so that the sensitiveness either increases or decreases in the course of time. Potassium was placed in bulb M, Fig. 4, distilled into K and poured through funnel F into final position C in cell No. 4. The surface of the potassium be- came darkened to a reddish pur- ple color, as the cell was left ex- UWE LENGTHS ,54 60 Fig. 7. posed to the light of the room for six days before the observa- tions, shown in Table II. and curves of Figs. 7 and 8 were taken. TABLE II. Cesium Cell No. 4. t = 23 C. Wave-length. MM Frequency 2 . A 2 10 80 Volts. V Wave-length. MM Frequency 2 . A'2 I0 30 Volts. "V 420 .510 1.070 600 .250 0.394 450 .444 0.890 630 .227 0.356 480 .391 0.730 660 .207 0.335 510 .346 0.609 690 .189 0.279 540 .309 0.523 720 .173 0.249 570 .278 0.472 750 .160 0.243 Qft Volts on needle of electrometer- 12 7. Km = .00150. These curves are very significant. The curve of Fig. 7 certainly is not a straight line as Planck's law would require, but Fig. 8 shows a straight line within a reasonable error of observa- tion. There is a slight varia- tion in the points near the red end of the spectrum, but that is probably due to the great difficulty of determining those points accurately. It was found that the maximum equilibrium potential was in- dependent of the intensity of the incident light, within the limits of the FREQUENCY 22 J4 Fig. 8. VOL. I.] No. i. J VELOCITY OF ELECTRONS. full intensity due to the arc, and the intensity of the light due to an incandescent lamp directed upon the cell. Cell No. 8 was a cell in which the active metal was potassium fixed with hydrogen. It was similar to Fig. 3. The potassium was dis- tilled upon a platinum plate (which had iron attached) at position B, Fig. 3, and moved into position C by means of a magnet. The electrode distance was about 2 mm. The potassium was fixed in the usual manner, as described before, but was not photo-electric. The movable electrode was moved back to position B and the potassium WAVELENGTHS 34- 60 Fig. 9. 50 melted. When the electrode was removed back to position C, it was photo-electric. Observations were made upon the cell for three consecu- tive days, which indicated a positive potential of the alkali metal when exposed to light. The potential was erratic however. Nine days later consistent observations were made upon the cell as shown in data of Table III., and Figs. 9 and 10. TABLE III. CcBsium Cell No. 8. t = 23 C. Wave-length. MM Frequency 8 . N* 1030 Volts. v Wave-length. MM Frequency 2 . N* Volts. V 420 .510 .835 570 .278 .407 450 .444 .722 600 .250 .361 480 .391 .622 630 .227 .348 510 .346 .537 660 .207 .326 540 .309 .488 690 .189 .266 Volts on needle of electrometer 106. K m = .00141. These plates show the same characteristic properties of the phenome- non. The equilibrium potential is proportional to the square of the DAVID W. CORNELIUS. [SECOND L SERIES. frequency. This is always the case when the metal is in the permanent state of activity. Caesium was poured into position C in cell No. 13, which was of the form shown in Fig. 4. The surface was "fixed" in the usual manner. The color of the surface was a greenish gray and partly bronze. When WAVL LENGTHS WftV LENGTHS Fig. 11. 54 60 Fig. 12. 72- liquid air was applied to the charcoal bulb, the metal was not active in the beginning. Violet light was incident upon the cell for an hour, or more, before the electrometer indicated a positive deflection of 510 mm. which is equivalent to .062 volt. A set of observations was taken, as recorded in curve I of Fig. n. The maximum potential was reached very quickly after the metal was connected to the electrom- eter, but was very difficult to read accurately. Liquid air was kept continuously on the 0.31- ^ ^^ ^ bulb and a series of observa- tions was taken about twelve hours later, as recorded in curve 3, Fig. II. About nine hours later another series was taken as shown in curve 3 of the same figure. The cell was left un- disturbed for four days (due to a lack of liquid air). After this time another series of observations was taken upon the cell as given in Table IV. and curve I of Figs. 12 and 13. (The time required for the completion of a series is about two hours.) Then following this series another was immediately taken, Table IV. and curve 2, Figs. 12 and 13. The cell was placed in an ice bath and another set of observations for o C. was taken which is recorded in Table IV. and curve 3 of Figs. 12 and 13. Two VOL. I. No. i. VELOCITY OF ELECTRONS. days later sets of data were taken for variation in temperature as shown in Table V. TABLE IV. Casium Cell 13. 4 days later than Fig. 11. X = wave-length. N 2 = frequency 2 , v = volts. \ N* Time, 3 P. M. Tern., 23 C. V Time, 6 P. M. Tern., 23 C. v Time, 10 P. M. Tern., o C. v 420 .510 .468 .414 .604 450 .444 .392 .373 .520 480 .391 .355 .368 .470 510 .346 .301 .342 .420 540 .309 .259 .305 .382 570 .278 .220 .272 .345 600 .250 .197 .249 .306 630 .227 .168 .228 .288 660 .207 .145 .220 .248 690 .189 .132 .204 .204 Volts on needle of electrometer 127. K\yj = .00120. TABLE V. Casium Cell 13. 2 days later than Figs. 12 and 13. X = wave-length. N 2 = frequency 2 , v = volts. A N* Tern., 23 C. v Tem.,40C.(?) V Tern., o C. v 420 .510 .475 .600 1 450 .444 .405 .528 l 480 .391 .378 .486 .483 510 .346 .348 .450 .455 540 .309 .318 .414 .420 570 .278 .288 .367 .374 600 .250 .258 .342 .348 630 .227 .242 .294 .298 660 .207 .228 .248 .256 690 .189 .205 .212 .214 Volts on needle of electrometer 127. Km = .00120. The curves of Fig. n indicate a change with time similar to Fig. 6. There seems to be a growth in the sensibility of the cell as well as a smoothing of the curves. The surface of the photo-electric metal seems to undergo a change until it finally reaches a steady state, in which the maximum potential varies as the square of the frequency of the incident light. 1 Reading of the electrometer uncertain. Possibly rise of the temperature of the cell, poor insulation, and negative effect are the causes of the difficulty. The cell, in this case, became negative in a very few minutes when in the dark. 26 DAVID W. CORNELIUS. HEWES! The set of curves I and 2, in Figs. 12 and 13, shows the cell to have reached a steady state. It is interesting to note the development of the cell. There is some suspicion to believe that the sensibility increases within the length of time (two hours) required to make a set of observa- tions. Curve 2 is read from the red to the violet end of the spectrum. Curve 3 for ice temperature is a little uncertain at the end points, the electrometer being difficult to read in that region. All the errors, im- perfect insulation, rise of temperature of the cell, etc., tend to lower the points. There is a little uncertainty, therefore, as to the character of curve 3, since the shifting of a few of the end points may be critical in determining the form of the curve. GENERAL RESULTS. Let us consider the significance of this experimental work. We see that Planck's law, which states that the maximum potential acquired by the alkali metal should be proportional to the frequency of the incident light, is not corroborated. But, on the other hand, the maximum equilibrium potential of the metal P varies as the square of the frequency n of the light. This relation is expressed by the equation, P = kn* + Po, where k is a factor of proportionality and Po a constant. The theory, as developed by J. Kunz, 1 is expressed in the form E = kri*, where E is the energy of the vibrating Faraday tube in the beam of light, k is a factor of proportionality and n the frequency of the light. If light falls upon a photo-electric metal a part of the energy is reflected and a part absorbed, both being proportional to the square of the frequency. In order that an electron may escape from the metal, its kinetic energy must be sufficient to overcome the attraction of the positive charge left behind. An elec- tron, in passing through the metal, may lose some energy by collision with molecules of the metal before it reaches the surface. Let us call this loss of kinetic energy w. Then the electron leaves the surface of the metal with a kinetic energy E = kn 2 w. The metal acquires a positive charge and a maximum potential of P, when the electrons are escaping, which is in equilibrium with the energy of the escaping electrons. If the charge of an electron is e, then Pe = akn 2 w. We are able to calculate the values for the constant w, from the experimental observations. The straight lines of Figs. 8, 10 and 13, which represent the relation of maxi- mum potential and square of frequency, may be expressed in the form P = sri* + w. 1 J. Kunz, PHYS. REV., Vol. 29, 3, 1909. VOL. I.I No. i. J VELOCITY OF ELECTRONS. If P = o, then sn 2 = w. Thus graphically w is the point where the curve crosses the y axis, if P = y and x = n 2 . Several values have been calculated from the data which are given in the table below. The method of calculation may be made clear by a sample calculation taken from Fig. 13, Pi -P. 5 = where PI is potential in absolute units for a frequency i, and P 2 is the potential in absolute units for a frequency n z . This gives Pi - P 2 * X 300, where P\ and PI are expressed in volts. (.468 - .132) s = 300 X .51 X io 30 - :i8 X io 30 * X io- 32 for the slope of curve I, Fig. 13. Applying this value in the formula for the case where X = 420^ w = P l - sn? = .468 - (.34 X io- 32 X .51 X io 30 X 300) = .052 volt = .174 X io~ 4 abs. e X w = 4.65 X io- 10 X 174 X io- 4 = - .0807 -io- 12 ergs. This represents the energy lost by the electron in reaching the surface or the amount of work necessary to drag an electron to the surface of the metal. VALUE OF WORK TO BRING ELECTRON TO SURFACE. TABLE VI. Metal in Cell. Caesium 23 C. Caesium o C. Caesium 23 C., 48 Hrs. Later. Pot. Cell No. i. Pot Cell No. 8 with H. Values of 5 X 10~ 32 . .340 .368 .273 .817 .574 .344 .376 .273 .827 .575 .338 .369 .272 .822 .563 .346 .370 .277 .833 .573 .340 .369 .270 .847 .575 Mean 5 X 10~ 32 . . . .342 .374 .273 .829 .572 Work in volts .052 +.037 +.057 - .160 -.041 Work inergsXlQ- 13 -.807 +.572 +.888 -2.480 -.667 The velocity of an electron emitted from the surface is given by the equilibrium relation Pe = ]^>mv 2 , where P is the maximum potential, e 28 DAVID W. CORNELIUS. [SECOND [SERIES. the charge of the electron, m its mass and v its initial velocity of emission from the surface. Hence m gives the formula for the calculation of the velocity where e/m is 1.77 X io 7 and P has values as determined by observations. VALUES OF INITIAL VELOCITY OF ELECTRONS. TABLE VII. Cell. A in nn. PAbs. Units. v= t^p, . \ m ' sec Pot. No. 4 420 1.09 X IO 8 6.21 X IO 7 Pot. No. 4 690 .266 X IO 8 0.97 X IO 7 Pot. No. 4 Pot. No. 8 750 420 .233 X IO 8 .835 X IO 8 0.91 X IO 7 5.45 X IO 7 Pot. No. 8 Caesium No. 13 with H Caesium at 23 C. 690 420 690 .266 X IO 8 .472 X IO 8 .780 X IO 8 0.97 X IO 7 4.09 X IO 7 0.78 X IO 7 At ice 420 600 X IO 8 4.61 X IO 7 At C 690 .177 X IO 8 0.79 X IO 7 Planck's law as expressed by the equation, E = hn = which may be written + C, hn = Pe + C, gives the right order of magnitude for the velocity of the electron although it does not express the relation of the velocity of the electrons as a function of the frequency of the incident light, h has a value of 6.548 X io~ 27 ergs sec. The velocity is given by the equation (i) v = 1/2/m/w. For light of wave-length 420^ n = 0.715- io 15 . The mass of the electron is 8.7 X io~ 28 grams. These values applied to the formula give \2hn == W ^ = 2 X 6.55 X io- 27 X7i5 = I0 ' 3 x I0 cm * sec * This compares well with the experimental values. However, the experimental values for the maximum potential acquired by the metal, for light of different frequencies, are different from those calculated by means of the equation of Planck, hn = Pe + C, where h is 6.5 X io~ 27 , e is 4.65 X icr 10 and C is 2.4 X io~ 12 . This varia- VOL. I.I No. i. J VELOCITY OF ELECTRONS. 2 9 tion of the experimental results from Planck's law is made clear by a set of calculations for potassium cell No. 8, which is shown in Table VIII. TABLE VIII. I0 Potential r, Calculated by Planck's Law, Volts. Potential Observed F 8 . Difference Fj F 2 Volts. .435 .266 .266 .455 .354 .326 .028 .476 .438 .348 .090 .500 .541 .361 .180 .527 .654 .407 .247 .556 .781 .488 .293 .588 .909 .537 .372 .625 1.063 .622 .441 .666 1.242 .722 .520 .714 1.440 .835 .605 The work done in expelling an electron can be computed. The work done in moving an electron of charge e\ (which must be equal to e% or a multiple of e%) through a distance dr is r dr dw = 72" dr ' The work done in moving the electron to infinity (i. 6., beyond the field of attraction of the atom) is : - CO dr 6162 e\62 7 = r = ~R' w where R is the radius of the atom. Now w ~- Hence J2 6162 iRm* This is the velocity necessary that the electron may escape from the metal. If an electron revolves about the positive atom it has kinetic energy due to its rotation. The velocity of the electron is determined by the equilibrium of the centrifugal and centripetal forces. If the electron has a mass w 2 , a charge e 2 , linear velocity v and the positive atom has a 3O DAVID W. CORNELIUS. mass mi, charge e\ (which must equal e^ or a multiple of e 2 ) and a radius R-, then I W2fl 2 I 6162 2~R~ = 2 R 2 ' if the revolution is in a circle, which is the case when mi is large as com- pared to w 2 . This gives T^T^ K.E. = F. A. Lindemann 1 has used this formula in his determination of the wave-length for which the selective photo-electric current reaches a maximum. Thus the work that has to be communicated to the electron by the incident light is the difference between the total work done in the expulsion of an electron and its energy due to rotation, viz., 1*14 ,,-K.E.-^. The values of the velocity, computed by this deduction, are near the values found by experiment. Suppose that e\ charge of the atom = e z = 4.65 X io~ 10 ,J = 5.35x10". Rk radius of potassium atom = 2.37 X icr 8 cm. used by Linde- mann. 2 2 X 4-65 X IP" 10 X 5-35 X io 17 7 cm. 2.37 X to- - = 4.58Xio' = velocity of the electron from potassium atom. The atomic volumes vary as the cubes of the atomic radii, so we have which determines the value of R c whenRk is known. R C8 = 2.75 X io~ 8 cm. Then 2 X 4-65 X I0 " 10 X 5-35 X IQl7 7 cm - 2.75 X io- 8 ) sec. = velocity of electron from caesium in order that it may escape. 1 F. A. Lindemann, Verh. der Deutschen Phys. Gesell., 13, No. 12, 1911. 2 F. A. Lindemann, Verh. Deutschen Phys. Gesell., 13, No. 12, 1911. 'i!'] VELOCITY OF ELECTRONS. 31 By means of the formula, the work necessary to expel an electron from the metal can be computed. Using values as in the above calculation, we get for the work which needs to be supplied by the incident light to expel an electron, in case of potassium, 1 44 I (4.65 X io- 10 ) 2 w - K.E. -*.- = 4.57 X io~ 12 ergs. 2 R 2 2.47 X icr 8 For caesium, v _ K. E . . K4.65X,o-y m 2 2.75 X IO- 8 The electron theory gives a means of calculating the time required for an electron to be emitted photo-electrically. The differential equation for the condition of resonance of the electron, when acted upon by an electrical wave, due to the vibration of the incident light, is d?xdx , dx 2e 2 /d 2 x\ 2 dx m dt*dt +aX Jt + 3c(d?) = cos ^' This may be written dE 2e 2 /d 2 x 2 dx E is the energy of the vibrating electron, e its charge, C the velocity of light, EQ the amplitude of the electric force in the light vector, times e, $ the frequency = 2-rrn, and x the displacement from the position of equilibrium. A particular solution gives x = h cos (t a). dx 2 e = -A* sin #-, ta = h = where is the frequency of the applied electrical force and is the frequency of the electron's vibrations. Introducing these values in the equation (i)[gives 2 e 2 I d 2 x 2 E 2 (f> cos / sin (t cos a cos t sin a) <&, put t = x, Jo . Then the integral becomes sin a-T/2. Hence, Since T = 2-rr, EC? sin is the work done in one revolution or complete vibration of the light vector considering the moving charge as unity. If the electron is in resonance with the light vector, then $ = and a = ir/2. Hence, ( sn air E = ~~ becomes 2 If the charge of the electron be taken as e instead of unity, as in the above consideration, the work dw done by the electric force is dw = E edx. Therefore, 2 7r 3 2 X 3 2e cm 2 g 16 7T 2 3 C The values for = 0.003 E.S.U. (estimated) and X = 420^ = 4.2 X io~ 5 cm., when substituted in the above equation, give This is the work supplied to the electron by one vibration of the light vector. It was found by means of the previous deduction that the work VELOCITY OF ELECTRONS. 33 necessary to liberate an electron is 4.2 X io~ 12 ergs. Thus we get the number of vibrations necessary to liberate an electron which is 4.2 X io- l: 1.3 X 10 _ 20 = 3 X 10*. Therefore, the length of time to liberate an electron is that required for 3 X io 8 vibrations of the light vector. For X = 420^, the time is X 4.2 X io- 5 / = C = 3 X io" = MX io- sec. Hence the time for 3 X io 8 vibrations is 3.1 o 8 X 1.4 X io~ 15 = 4.2 X io~ 7 second. Thus the time required for the liberation of an electron from a molecule by the incident light is very small. A conception of this period of time, however, can be obtained in terms of the distance, traversed by light in this interval, which is 3 X io 10 X 4 X io~ 7 = 120 meters. SUMMARY. The principal results of this investigation are as follows: 1. A small amount of residual gas in the photo-electric cell influences its behavior. 2. The surface conditions of the alkali metal has a very large influence upon the photo-electric effect; which may be constant from the beginning or increase or decrease in the course of time. 3. It takes, as a rule, some time for a cell to reach a steady state of sensibility. 4. The attempts to measure the velocities of the electrons by means of the magnetic deflection have been unsuccessful. 5. The results obtained indicate that the equilibrium potential depends to some extent upon the temperature of the metal, above zero degrees; below zero degrees the equilibrium potential seems to be independent of the temperature. Further experiments upon this point are necessary. 6. The relation of the velocity of the electrons and the frequency of the incident light is the same for: pure potassium, potassium "fixed" with hydrogen, caesium and caesium "fixed" with hydrogen. And the relation between the equilibrium potential and the frequency of the incident light is the more constant the nearer the metal approaches the permanent state of sensitiveness. 7. The theoretical and calculated values of the initial velocity of the electrons are both of the order of io 7 cm. per second. 8. The theoretical value of the time required for the expulsion of an 34 DAVID W. CORNELIUS. electron due to the resonance effect of the incident light is of the order of io~ 7 second. 9. The equilibrium potential of the electrons in the photo-electric effect varies directly as the square of the frequency of the incident light. Planck's law, according to which the units of the electromagnetic energy are proportional to the frequency is not confirmed by the results of this investigation. 10. While the theory of resonance shows that a beam of light may supply a sufficient amount of energy for the electron to escape it cannot satisfactorily account for the essential fact that the velocity of the elec- trons escaping from the metal is proportional to the frequency. The author takes great pleasure in acknowledging his indebtedness to Professor A. P. Carman for the facilities for this investigation and to Professor Jakob Kunz, both for his general supervision of the work and for many valuable suggestions. LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS. May 6, 1912. {Reprinted from the PHYSICAL REVIEW, N.S., Vol. I., No. 3, March, 1913.] IONIZATION OF POTASSIUM VAPOR BY ULTRA-VIOLET LIGHT. BY S. HERBERT ANDERSON. THE general method of determining the ionization of potassium vapor by ultraviolet light consisted in measuring the current produced be- tween two electrodes which were contained in a highly exhausted tube con- taining potassium vapor, when a given potential difference was applied across the electrodes and a beam of ultraviolet light passed through the vapor between the electrodes. The form of the tube used is shown in Fig. I, A. The tube was 4 cm. Fig. 1. in diameter and 12 cm. long. It was closed at one end with a quartz plate sealed on with Bank of England sealing wax. The opposite end of the tube was drawn down to about 8 mm. diameter and terminated in a bulb b in which the potassium k was lodged. The smaller tube was bent around in a semicircle to prevent particles shot off from the potassium from penetrating directly the space between the electrodes. The potas- sium introduced into b was obtained by distillation and was perfectly pure and clean. The tube was exhausted by a Gaede pump and then by a charcoal bulb and liquid air to the best possible vacuum. The elec- trodes, e\ and e 2 , were platinum plates 6 X 2.5 cm., and were placed parallel to each other 3 cm. apart. 2 34 5. HERBERT ANDERSON. [!ER?E S D In order to test the ionization at temperatures higher than room temperature the tube was placed in an electric furnace consisting of a copper cylinder on which were wound two layers of wire so connected that the magnetic field within was negligible. The electric furnace containing the tube was placed in a sheet iron box, tightly closed except for a slit 5 X 30 mm. at one end, which could be opened to admit ultraviolet light. This metal box was connected by a metal tube to a tight metal cylinder in which a Dolezalek electrometer was placed. Electrode e\ was con- nected to one pair of quadrants of the electrometer. Electrode 6% could be grounded or connected to one terminal of a battery, c is a metal collar about the tube where electrode ei is sealed in. This was grounded so as to prevent conduction over the outside of the tube from effecting the electrometer. The copper cylinder of the heating coil and the metal containers of the heating coil and electrometer was grounded, E. When the tube was kept in darkness at room temperature, 25 C., no current could be detected with the electrometer when a potential differ- ence of 1,000 volts was maintained between the electrodes. When a beam of ultraviolet light from a spark between zinc electrodes was passed into the tube, but not striking the electrodes, and the same potential difference, 1,000 volts, was maintained, e% being connected to the positive terminal of the battery, there was still no current. (The electrometer was capable of indicating a current of io~ 13 amperes.) If however the beam of light was incident upon the electrode connected to the electrom- eter, there was a deflection and the direction of the current was from e z to e\. This of course was due to the photo-electric action of the plati- num electrode. Hence there was no indication of ionization at a tem- perature of 25. The tube was then heated to 55, which is the highest temperature to which the sealing wax may be heated without softening. Two hours was required for this heating, in order to get a constant temperature. At this temperature when a beam of ultraviolet light was passed between the electrodes there was a comparatively large current, the values of which for different potential differences are given in column (a) of the table. It was found that these readings could not be duplicated but that the current increased as the tube was maintained at this temperature. After four hours another set of readings was taken which is given in column (&). The tube was then allowed to cool down to room temperature and the conductivity tested when a beam of ultraviolet light passed between the electrodes. The current was found to be about the same as that found by the last set of readings at 55, as is seen by comparing column (c) with column (b) (Fig. 2). VOL. I.- No. 3. J I ON I Z AT I ON OF POTASSIUM VAPOR. 2 35 The tube was in perfect condition after the heating. The vacuum was tested by a spark discharge and found to be at the Rontgen ray stage. The discharge showed some of the characteristic color due to potassium vapor. In the table the current is given in terms of the rate of deflection of the electrometer needle in mm. per second. A deflection of 20 mm. per second corresponds to a current of io~ 12 amperes. The current observed is surprisingly large if one takes into consideration the fact that at 55 the vapor pressure of potassium is not large. The minimum current observed TAfllg ffiSwS 76.0 1S6.0 187.0 Fig. 2. was 1.5 X io~ 12 ampere, that is, an order of magnitude quite different from the currents due to ionization of any other vapor or gas by ultra- violet light. The increase of conductivity as the tube was maintained at a tem- perature of 55 is not easy to explain; nor the fact, that when the tube had cooled to room temperature the conductivity was about the same as that last observed at 55, while in the first place there was no current at room temperature. However, it is likely that this is closely connected with the phenomenon observed by Wood 1 in the resonance spectra of mercury vapor. He found that there was a true absorption of light only when the pressure of the gas was above o.oi mm. When a small amount of air was introduced so that the pressure was raised above o.oi mm. the absorption increased with the pressure. It is not unreasonable to expect that ionization accompanies the transformation of light energy into heat energy that occurs in true absorption. If this is the case an introduction 1 Phil. Mag., V., 23, p. 689, 1912. 236 5. HERBERT ANDERSON. [IS?*!! of a small amount of air or other gas into the tube of this experiment would result in an increase of conductivity. In this experiment it is very probable that gas was given off from the electrodes and walls of the tube as the temperature was maintained at 55. On the basis of Wood's discovery this then would account for the increase in conductivity. No deposit of potassium was observed in the tube, after the temperature had been raised to 55. Moreover, if there had been a deposit of metal, it would have occurred during the distillation, as the temperature was then above 200, and yet no conductivity or ionization was noticeable until the tube was heated to 55. It is the intention of the author to extend this investigation and determine this point. SUMMARY. 1. Potassium vapor at 55 is readily ionized by ultraviolet light. 2. An increase of ionization is produced by the addition of a small amount of foreign gas. The writer is indebted to the Laboratory of Physics of the University of Illinois for the facilities and to Dr. Kunz for suggestions for the above work. UNIVERSITY OF WASHINGTON, November, 1912. (Reprinted from the PHYSICAL REVIEW, N.S., Vol. I., No. 3. March, 1913.] RECTIFYING PROPERTIES OF A PHOTO-ELECTRIC CELL. BY S. HERBERT ANDERSON. TT has long been known that a photo-electric cell in which electrons * are freely emitted from a metal under the action of light has distinct rectifying properties. In some investigations by Professor Kunz and Dr. J. G. Kemp it was found that in a photo-electric cell of the type used by the author in the present investigation may be used as a detector of electric waves. When used in connection with a Fleming cymometer it was found much more sensitive than the neon tube furnished with the instrument. Since its use as a detector depends upon its rectifying property, the present investigation was undertaken to determine the adaptability to practical use in wireless telegraphy. DESCRIPTION OF METHOD AND APPARATUS. The form of the photo-electric cell used is shown in diagram by Fig. i, A. One electrode is a hemispherical cap of pure potassium deposited in the lower part of bulb a, which is 4 cm. in diameter. The other elec- trode is a platinum point b, the distance of which from c can be adjusted by the action of a magnet on the iron ring d. The method of preparing the potassium was the same described in a former paper. 1 The potassium collected in e Was poured into bulb a and deposited on the lower half by distillation. It was desired to have the cell as stable as possible and to this end nitrogen was introduced into the tube A. For removing all traces of oxygen and water vapor from the nitrogen, tube B, Fig. i, was used. Before the evacuation of the system a piece of potassium was introduced into the tube at / which was then sealed off. When the tube was evacuated the potassium was dis- tilled so as to form a brilliant metallic surface all over the inside of B. With stopcock g closed, dry nitrogen was let into B through h at atmo- spheric pressure. The potassium near h turned black showing some oxidation, h was closed and the tube heated until again there was a bright metallic surface. This insured the removal of all oxygen from the gas. Then g was opened and nitrogen let into A . g was closed and the tube A pumped out until the discharge from a small induction coil passed 1 PHYSICAL REVIEW, XXXV., p. 239, 1912. 223 5 - HERBERT ANDERSON. easily between the electrodes b and c. Thus in a rough way the pressure of minimum sparking potential was obtained. When a potential of 220 volts of a 6o-cycle alternating current was applied no discharge occurred, but with 330 volts a current of about o.i ampere passed. A was then sealed off from the pump at k. The method used in examining the rectifying properties of the cell was the same as used by Pierce 1 in examining the crystal and electro- lytic detectors and is shown in diagram by Fig. 2. The image of the luminous spot of the fluorescent screen of a Braun tube is brought to a focus on a drum d by means of a lens /. This drum is connected directly to synchronous motor which operates on a no- volt, 6o-cycle alternating current. The drum is covered with a sensitive photographic film and is enclosed in a light-tight box. The source of the current sent through the photo-electric cell A was a 44o-volt, 6o-cycle alternating current supplied by the same dynamo that furnished the no-volt circuit that the motor was operated upon. Thus the frequency of the two circuits was the same. By means of a potentiometer scheme P any potential dif- ference up to 455 volts (which was the potential across the so-called 440 mains), could be applied to the electrodes of the cell. Connected in series with A were a pair of electromagnets, c\ and c%. These were placed, one above and the other below, the Braun tube, with their axes in a vertical plane, so as to give a horizontal deflection to the narrow cathode beam which passed through the small hole in the metal screen s. The total resistance of the electromagnets was 381.8 ohms. They were fitted with cores of soft Swedish iron, }/% inch in diameter. By means of a double throw switch 5, the photo-electric cell could be replaced by a non- inductive resistance R which was adjusted to allow the same current to go through the electromagnets as passed when the cell was in the circuit. An electrostatic voltmeter V gave the fall of potential across the electrodes of the cell. METHOD OF TAKING OSCILLOGRAMS. In Plate I., (a), (>), (c), are shown three of the oscillograms taken, These were obtained in the following manner: a photographic film was placed on the drum d, Fig. 2, the box closed and a cap put over the lens; the motor was started and adjusted to run in synchronism; the switch 5" was then closed so that the alternating current potential was applied at the electrodes of the cell (the current which passes through the cell also goes through the electromagnets and the alternating magnetic field produced causes an alternating deflection of the cathode beam, so that the spot of light on the fluorescent screen is drawn out into a horizontal 1 PHYSICAL REVIEW, XXVIII., p. 153, 1909. No" 3 L ] PROPERTIES OF A PHOTO-ELECTRIC CELL. 224 line) ; the cap was then removed from the lens and the image of the spot of light moving on the screen was thrown upon the photographic film. The drum was rotated in synchronism and made a complete rotation for every two cycles of the current. So the spot of light moved over the film with two motions, the horizontal motion being produced by the changing magnetic field and the vertical motion produced by the move- ment of the drum. The spot of light started in at the same point at the beginning of each rotation. The part of the oscillogram obtained by this much of the exposure is the heavy line showing loops only above the horizontal axis, that is, a current in one direction only. The switch was then thrown so that R was in the circuit instead of A . The part of the oscillogram due to this exposure is the sine curve. The switch was then opened so that no current went through the electromagnets and conse- quently there was no horizontal deflection. This exposure gives the line of the axis of abscissas, the axis of zero current. The time of exposure for oscillogram (b) for the curve of the rectified current was 2.5 minutes; for the non-rectified current, 1.5 minutes; for the line of the horizontal axis, 40 seconds. So for the total exposure the spot of light moved over the film 8,400 times. This shows that the motor was running in syn- chronism. For oscillograms (a) and (b) the ordinary Eastman kodak films were used. For oscillogram (c) an Eastman extra rapid film was used. The times of exposures for the three curves of this were i' 50", 50" and 30" respectively. Probably i', 30" and 20" would be plenty of time. The lines are all heavy except in one place, where the film may have been defective or was not evenly developed. The curve obtained when the current passed through the ohmic resistance R may be called a potential phase curve. It is of course a current curve, but since the potential across the ohmic resistance is in phase with the current through that resistance it gives us the phase of the potential about the photo-electric cell, and enables us to determine whether or not there is any lag or advance of the current through the cell. It will be noticed that in every case that the maximum point of the rectified curve is less than that of the potential phase curve. This occurs in spite of the fact that in every case great care was taken to adjust the resistance R before the exposure for an oscillogram so that the maximum deflection of the cathode beam was the same for the current passing through R as it was for the current passing through A. But as the cell is used, that is, as a current passes, the resistance of the cell seems to increase, and consequently the deflection of the cathode beam decreases. This is shown by the broad line of the curve of the rectified current in 22 5 S. HERBERT ANDERSON. [SECOND [SERIES. oscillograms (a) and (c) especially. During the exposure for each of these curves the current decreased about 0.5 milliampere, or 10 per cent. This increase of the resistance seems to come about by an absorption of the gas (nitrogen) in the cell. The character of the glow discharge changed in such a way as to show a decrease in pressure. The effect seemed to be much the same as that which occurs with a glow discharge through hydrogen with a potassium cathode in which potassium hydride is formed. But with this difference, that in the cell with hydrogen the potassium hydride formed is of a deep violet color, becoming almost black if the discharge is continued for a long time. But with the cell containing nitrogen the color taken on by the potassium under the action of the glow discharge is at first bronze, and with a continuation of the discharge the color becomes a bright blue, with just a suggestion of a greenish tinge. On heating the cell until the potassium is melted the color disappears, the potassium assumes its original bright metallic luster and the pressure is increased. It seems very probable that a potassium nitride is formed by the glow discharge. Since this work was done a reference 1 has been found giving an account of the formation of potassium nitride by a glow discharge between a potassium cathode and silver anode immersed in a mixture of 90 per cent, liquid nitrogen and 10 per cent, liquid argon; and also the account states that the nitride is formed when the liquid nitrogen is replaced by gaseous nitrogen. Fig. 2. In taking all these oscillograms the amount of light falling on the photo- electric cell was rather faint. There was an eight-candle-power red- globed, incandescent lamp about three meters distant from the cell; and the cell was exposed to the faint light from the Braun tube. It was noticed just after oscillogram (b) was taken that light falling on the cell had a marked effect on the action. If the cell was in total darkness and 1 Ber. der deutschen Chemischen Gesellschaft, Vol. 43. p. 1465, 1910. PHYSICAL REVIEW, VOL. I., SECOND SERIES. March, 1913 PLATE I. To face page 226 S. HERBERT ANDERSON VOL. I. No. 3. . PROPERTIES OF A PHOTO-ELECTRIC CELL. 226 the potential applied there was no discharge in the tube and no measurable current passed. But if a i6-candle-power lamp at a distance of a meter was turned on the discharge occurred and continued after the light was turned out. But by the deflection of the cathode beam it was noticed that the current was about 6 per cent, less when the cell was in darkness than when it was illuminated by the i6-candle-power lamp at the distance of I meter. If however the lamp was brought up to a distance of 40 cm. from the cell, the discharge stopped, but started again when the light was moved away. This shows that the light intensity has a very marked effect, as well as the gas pressure and the electrode distance. It is very Fig. 3. probable that the discharge continued after the light was turned out be- cause of the action of the light produced by the discharge in the cell upon the potassium. TABLE I. Oscillogram. / in Amperes. FR.M.S. Value in Volts. Electrode Distance (in Centimeters). (a) 0.004 390 4.1 W 0.005 455 4.7 (<0 0.003 370 4.7 DISCUSSION OF OSCILLOGRAMS. In Table I. are given the maximum values of the rectified current, /; the R.M.S. voltage across the electrodes, F; and the electrode distance for each oscillogram. The divisions of the scales along the oscillograms represent milliamperes. Time is represented in a horizontal direction from left to right. 227 5 - HERBERT ANDERSON. The characteristic features of the oscillograms are: (i) That the recti- fication is complete, that is, the current is transmitted in only one direc- tion ; (2) the form of the current curve in the rectified cycle ; (a) there is a lag in rising from the axis of zero current ; (b) the curve up to the maxi- mum point is nearly a straight line ; (c) the curve of decreasing current is of an exponential form; (d) the lag at the end of the half cycle is very much less than at the beginning, just how much is difficult to determine because of the exponential form of the curve. The degree of rectification in this type of cell is shown by another experiment. A cell of the same form and dimensions, but employing potassium hydride as the active electrode and hydrogen for the gas was tried with a direct-current potential. 400 volts had to be applied at the electrodes before a current would pass which could be measured by a milliammeter. With this potential there was a glow discharge in the tube. When electrode c, Fig. I, was connected to the negative terminal of the battery and b to the positive, the current was 100 milliamperes. When the terminals were reversed, the current was 0.05 milliampere. The current then passing in one direction was 2,000 times as great as the current in the opposite direction. Such a ratio is much larger than could be shown by the oscillograms. In general the cause of rectification in this kind of a cell is readily explained. When the potassium electrode is connected to the negative terminal of the source of potential and the platinum point to the positive, electrons are given off readily by a photo-electric action. With such a potential as was used a very faint light is sufficient to start the discharge of electrons. When the field is in the opposite direction no electrons can be given off when the potential difference is greater than that arising from the photo-electric action. However the current due to the electrons alone is of a very much lower value than that obtained here. The author found (1. c.) the electron current from a potassium electrode of about one fourth the area used in this experiment was 6 X io~ 10 amperes for the same electrical field. However the light intensity was much greater than in the present investigation. But assuming that the number of electrons leaving unit area of the potassium electrode is the same in the two cases, and hence, that the current due to the electrons in the present investiga- tion is about 24 X io~ 10 amperes, even then this is insignificant compared with the total current. So the carriers of the current must be chiefly ions which are produced by collisions of the electrons with the mole- cules of the gas. As the potential across the electrodes rises from a zero value to a maximum, c being negative and b positive, the current that can be detected is negligible until the potential difference reaches such a No L ' 3 L ] PROPERTIES OF A PHOTO-ELECTRIC CELL. 22% value that the electrons have sufficient velocity to produce ions by collision. This is indicated by the point where the current curve rises sharply from the axis of zero current in the oscillograms. From this point on as the potential increases to a maximum there is a two-fold increase in the conductivity due (i) to the increase in the rate of production of ions and (2) the increase in the velocity of the ions. As the potential de- creases the conductivity decreases in a two-fold manner. Thus we see that the current will not be a sine function because the resistance is not a constant. It is not possible to determine analytically the form of the current curve until the function which shows how the resistance varies is known. When the potential falls below the critical value necessary for the production of ions there are some ions still left in the space between the elecrtodes, and the current from this point on until the potential becomes zero is due to the movement of these ions to the electrodes. When the impressed E.M.F. reverses and c becomes positive and b negative, the electron current is zero, and hence the source of ionization is zero and there is no current. By the application of the equations for alternating currents we can determine whether the characteristics of the current curve are due to any of the factors of the circuit besides the photo-electric cell. The potential phase curve was obtained when the circuit contained only resistance and the self-inductance of the magnetizing coils. The dif- ferential equation of such a circuit with an impressed, simple, harmonic E.M.F. is Rii + L~ = sin co/, (i) at the solution of which is When the current has reached a steady state the exponential term becomes negligible. Of the constants of the circuit R and co are known, but L is not. This may be determined by taking the expression for the maximum value of ii The R.M.S. value of the voltage across the electromagnets was 1.5 volts at the time oscillogram (b) was taken. The maximum value of the cur- rent, taken from the oscillogram, was 0.005 ampere. The resistance of the coils was 381.8 ohms. The maximum voltage is given by ' = 2.12 VOltS. 0.707 229 5 - HERBERT ANDERSON. We may then obtain Leo from (3) , where E is the maximum voltage across the coils and R is the resistance. 2.12 = l/ (381.8)'+!^' Leo = 184.4. In order to obtain the potential phase curve a resistance of 82,800 ohms had to be introduced into the circuit in place of the cell. The angle of lag of the current in this circuit behind the impressed E.M.F. is given by Leo arc tan , (4) where R is the total resistance of the circuit and is 82,800 + 382 ohms. Leo 184.4 arc tan - = arc tan = 0.128 . R 83,182 That is, the lag of the so-called potential phase curve behind the impressed E.M.F. is 0.128. From measurements on oscilligram (b) it was deter- mined that the current in the rectified cycle lagged 0.109 part of a period or 39.24 behind the potential phase cycle. Hence the total lag of the rectified cycle behind the impressed E.M.F. is 39.24 + 0.128 = 39.368. We can find the voltage across the electrodes at which the current rises above the axis of zero current by the expression e Q = E sin 39.368, where E is the maximum value of the voltage. The R.M.S. value of the voltage was 455 volts. 643.5 voits. - ;;;_ _ /: ..; e Q = 643.5 sin 39.368 = 408 volts. The equation for the current through the cell is given by diz E sin eo e r = R c i% + L -,, (5) where e r is the potential drop across the photo-electric cell. Since e r is a function of the current i% the form of this function must be known in order to integrate the above expression. This function is represented by the function potential curve. Unfortunately the author was unable to take such a curve with this cell. In Fig. 3 is shown a current potential curve taken by Dr. J. G. Kemp for a cell filled with hydrogen at 3 mm. No" 3 !'] PROPERTIES OF A PHOTO-ELECTRIC CELL. pressure and using an electrode distance of 3.0 cm. Undoubtedly the curve for the cell the author used was of the same type. The analytical expression for this curve has not been determined, but for certain regions of the curve the relation between the current and the potential can be expressed approximately by a linear equation. In the curve, Fig. 3, the maximum value of the current was about io~ 8 amperes, which is a much lower order of value than the currents obtained in this investigation. Hence it is very probable that the expression for e r for the range o.ooi to 0.005 ampere is e r = e + ri, (6) where e Q is the intercept of the axis of potentials and r is the resistance of the cell. Of course the resistance varies greatly and any value of r that might be determined would only hold for a small range of the current. Substituting the value of e r given by (6) in (5) we have di E sin co/ - e = (r + R c )i z + L . (7) Integrating this equation we get I m I co/ " E I Leo \ - r -+^t e sm I co/ arc tan ; =- 1 + ce L " . r+R, We may take e Q to be the voltage that must be placed across the electrodes before a measurable current will pass, that is, 408 volts. In order to determine a value of r, take the maximum value of i 2 from the rectified cycle. Then in equation (6) e r = E = 643.5 volts, iz = / = 0.005 ampere. Therefore 643.5 = 408 -f r X 0.005, r = 46,900 ohms. This then gives the resistance of the cell at the instant of maximum current. The exponential term in (8) becomes negligible within a very short time after the circuit is closed and hence should not occur in an equation dealing with current at the time the oscillograms were taken, when a steady state has been reached. It is apparent then that the current curve given by equation (8), when the exponential term is dropped out, will be a sine curve with a lag of arc tan Lco/(r + R c ) and with the axis of abscissae raised by an amount eo/(r + R c ). As previously pointed out the current curve cannot be a sine curve, hence we cannot use this 231 S. HERBERT ANDERSON. equation for determining anything about the current except at the instant of maximum value. We can determine then what the lag is at this instant. Leo 184.4 arc tan - ^r = arc tan = 0.224 . r + R c 47,282 This is the largest lag possible arising from the self-inductance of the circuit as r has a minimum value for the maximum value of the current. In as much as this angle is smaller than can be detected on the oscillo- grams, we may conclude that the lag in the current is due to the prop- erties of the cell as previously noted, and not to other factors of the circuit. Every electric wave detector of the rectifying type is of use as a detector either (i) because of its rectifying properties, or (2) because its current potential curve is not linear. 1 Inasmuch as the photo-electric cell possesses both of these properties it may be used in two ways, as Dunwoody 2 has shown crystal detectors may be used. In case the rectifying property is made use of the efficiency depends upon the degree of rectification. As in the photo-electric cell the power of rectification is of a very high order, it should prove as efficient as any detector used. It could be used either with a telephone or a sensitive galvanometer. It has the advantage of giving a glow-discharge when a current is passing, so the receipt of a call by wireless could be noted by the operator without the use of the telephone. The author is now attempting to find the most sensitive condition of the cell for detecting electric waves, and intends to test thoroughly its efficiency. CONCLUSION. 1. The rectifying power of a photo-electric cell, using potassium for the active electrode, has been found to be of the ratio 2,000 to I. 2. The general form of the rectified cycle is the same for the different pressures, electrode distances and potentials used. 3. The amount of the current for a given potential depends on the pressure of the gas, the electrode distance, and the intensity of light falling on the cell; but does not increase continuously with increasing intensity. 4. Nitrogen at a pressure of about 5 mm. combines with potassium or is absorbed by it when a glow discharge passes. 5. The high power of rectification and the high resistance of the photo- electric indicate that it may be very efficient as a detector of electric waves. 1 Fleming, Principles of Wireless Telegraphy and Telephony, p. 474. 2 U. S. Patent Specifications, No. 837, 616, 1906. No L ' 3 L ] PROPERTIES OF A PHOTO-ELECTRIC CELL 2 $2 The author takes pleasure in acknowledging his indebtedness to Dr. J. G. Kemp for the type of cell used and for the curve of Fig. 3, to Pro- fessor Kunz for many valuable suggestions and assistance in preparing the cells used, and to Professor Carman and the physics department of the University of Illinois, where the investigation was carried on, for the facilities and means for the work. PHYSICS DEPARTMENT, UNIVERSITY OF WASHINGTON, October, 1912. REPRINTED FROM ENGINEERING RECORD VOLUME 67, PAGE 265, MARCH 8, 1913 Air Currents and Their Relation to the Acoustical Properties of Auditoriums With Application of the Conclusions to Ventilating Systems By F. R. Watson, Ph.D., Assistant Professor of Physics, University of Illinois When looking up the references for the subject of architectural acoustics an ac- count was found of "some experiments made for the purpose of determining the effects of the currents of air within an auditorium upon its acoustical qualities." (W. W. Jacques. "Effect of the Motion of the Air within an Auditorium upon Its Acoustical Qualities." "Philosophical Magazine" (5), vol. 7, page in, 1879.) Jacques found by experiment that the ventilating system of the Baltimore Academy of Music was so arranged that it had a very pronounced action on the acoustics. He writes : "According to a survey, made with the thistle balls and the anemometer, of the space con- tained within the walls of this theatre, the movement of the air is as follows : The whole supply of fresh air is admitted at the back of the stage, is there warmed, then crosses the stage horizontally, passes through the prosce- nium, and then, somewhat diagonally toward the roof, across the auditorium in one grand volume and with gentle motion so as to almost entirely prevent the formation of minor air currents. It is exhausted partially by an out- let in the roof and partly by numerous regis- ters in the ceilings of the galleries. From this Fig. i central outlet and from the large flues of the registers, the air passes into the ventilating tower over the great chandelier, which sup- plies, in its heat, a part of the motive power of the circulation. . . . The acoustics are, if we may judge from the testimony of a large number of singers and speakers, as well as from our own observation, among the best. The weakest voice is audible to every seat in the house; sounds such as a sigh, a kiss, or even the simulated breathing of the somnambu- list, may be heard in the most distant parts; and all effects in music are exactly rendered. All singers and speakers agree in describing the facility with which the voice is used on this stage." Jacques carried out experiments to show that the acoustics were affected by the ar- rangement of the current of air. "For this purpose," he writes, "persons have been re- peatedly stationed at different parts of the. house during a performance, without being in- formed of the nature of the experiments to be carried out. They have been simply asked to note, at intervals during the evening, the comparative ease with which they could hear the performers. At various intervals during the evening the valves which control the venti- lation were reversed, so as to entirely inter- fere with the unbroken condition of the air and give rise to currents of circulation. Al- most invariably the testimony of the hearers would be that, at times corresponding to the interruption of the ventilation, the 'sound was dead, was confused and indistinct'; and it would be observed that people all over the house would make an effort to listen." This action of an air current seemed so re- markable that further confirmation was sought from other sources. The result of the search showed that both theory and experiment sup- port the results set forth by Jacques that an air current may affect the progress of sound waves, although the effect is small for ordinary conditions. It is further indicated that the ar- rangement of the ventilating system is one of the factors that may affect the acoustics of a room. Thus it can be shown theoretically that a stream of heated air can reflect and refract sound waves, the magnitudes of these effects being proportional to the temperature of the stream and to other less important factors. This deduction is supported by laboratory ex- periments and by conditions that have been noted in auditoriums. By means of the theory the experimental phenomena can be explained and the general conditions written down for the arrangement of the ventilation current that will be most beneficial for the acoustics. THEORY Lord Rayleigh has developed the general re- lations whereby the reflection and refraction of sound at the boundarv of two media may be Fig. 2 calculated. ("Theory of Sound," vol 2, section 270. See also equations at end of paper.) He shows that for perpendicular incidence at a surface between air and hydrogen about one- third of the energy is reflected. For the case of two layers of air, one at o deg. C. and the other at 10 deg. C., only about 83/100,000 of the energy is reflected much less than the case for air-hydrogen because the difference in density is correspondingly less. When the temperature difference between the layers of gas increases the amount of energy reflected also increases. Thus, for a difference of 27.3 deg. the energy reflected is 55/10,000; for 237 deg., 1/30 is reflected. Another instance of small density difference is the case for two layers of air at 10 deg. C., one of which is saturated with water vapor, while the other is dry. Only 1/744,000 part of the energy is re- flected. Rayleigh concludes that "reflections from warm or moist air must generally be small, though the effect may accumulate by repetition." For oblique incidence, however, more en- ergy is reflected than for perpendicular inci- dence. When the angle of incidence is suffi- ciently oblique, theory shows that total reflec- tion follows. Thus, for the case of two layers of air, one 10 deg. warmer than the other, the angle for total reflection is 79 deg. 7 min. ; that is, the angle between the direction of propagation of the sound waves and the sur- face of separation of the warm and cold air is 10 deg. 53 min. This means that waves must strike very obliquely for total reflection. For the layers of dry-moist air the angle is more oblique, namely, 86 deg. 8 min. for total reflec- tion. For less oblique angles the reflection is less, being practically zero for angles less than that for total reflection. In addition to the reflection that takes place at the boundary between two media there oc- curs also a refraction, or bending in direction, of the sound waves that enter the second medium. For instance, a beam of sound waves striking obliquely at the boundary between cold and warm air would be bent toward the bound- ary as it enters the warm air. A number of experiments are cited that con- firm the theory. Tyndall showed that a high- pitched sound was easily reflected by the flame of a bat's-wing gas burner. (Tyndall, "On Sound/' 1898 edition, page 319.) For this case the temperature difference between the air and the flame is great, so that the density difference is also great, and a large reflection would be expected. The author has repeated Tyndall's experiment for conditions somewhat different. Sound waves of about 2 cm wave length were generated by means of a Galton whistle and directed against the vertical sheet of hot gas rising above a straight row of gas flames. The waves were reflected by the gas column and detected with a sensitive flame for both per- pendicular and oblique incidence. Sabine describes an interesting case that shows the effect of heated currents of air in a room. (Engineering Record, vol. 61, page 780, 1910.) In a court room in Illinois a stove was situated in the center of the room. In winter when the stove was heated great diffi- culty in hearing the judge's remarks was ex- perienced by those whose position was such that the stove stood between them and the judge. In the summertime, when the stove was not in use, the trouble disappeared. The ex- planation of the effect follows from the pre- vious theory. The ascending column of air from the stove was so hot that it reflected and refracted the sound to such an extent that little was left to pass on directly to the audi- tors in the rear of the room. Tyndall describes another experiment in which he placed a series of gas currents be- tween a source of sound and a receiver. ("On Sound," page 312.) The sound was entirely cut off. Suppose A (see Fig. i) to be the source of sound and B the receiver. A was a bell of high pitch and B a sensitive flame. At the places marked -f- imagine currents of illuminating gas to rise. At places marked imagine descending currents of cold carbon dioxide. As the sound goes out from A, a portion is reflected back from each boundary between the gas columns, so that finally there is little or no sound left that gets through to B to affect the flame. In this case a large effect is to be expected, since the densities of the gases are very different. APPLICATION TO STREAM OF AIR IN AN AUDITORIUM The previous theory may now be used to ex- plain the effect of a current of air such as the one investigated by Jacques in the Baltimore Academy of Music. Assume that the current of air is 27.3 deg. (for convenience of calcula- tion) warmer than the air' in the room, and that it moves in one large stream from the stage to the walls at the rear of the auditorium. Calculations show (see theory at end of paper) that the sound waves that strike the boundary between warm and cold air are practically all transmitted except for those waves that strike very obliquely. These latter waves become totally reflected. The transmitted waves are bent in direction as they pass into a medium of different density. The state of affairs is indi- cated in Fig. 2. Inspection shows that the ef- fect of the air current is to bend the sound in the direction of the stream, but this effect is seen to be small. We now pass to the case of the haphazard currents and attempt to explain why Jacques found the sound confused and indistinct. For this case there are a number of currents of air of different densities, with many boundaries set up between hot and cold gases. Each boundary has its effect in reflecting and re- fracting the sound waves so that the resultant effect is complex. Furthermore, if it be con- sidered that these currents are not steady, but that each one fluctuates more or less, it is seen that the effect at any one point, say the ear of the observer, is "confused and indistinct." The result is much the same as the analogous case in optics where, on a summer's day, objects at a distance appear quivering and distorted because of the intervening ascending currents of warm air. So in the auditorium the sound which is clear and distinct after passing through a homogeneous medium may well be- come distorted when it goes through a num- ber of unsteady streams of unequally heated air. * Jacques' experiments bear out this conclu- sion about the indistinctness produced by tiie varying currents. He writes that 10 to 15 min- utes were required for the air currents to be- come steady after the ventilation had been re- versed. During this time of unsteady currents the observers reported the hearing confused and indistinct. This last conclusion is confirmed by a num- ber of experiments. Jacques set up an ap- paratus so that the sound of an organ pipe was diffracted to the rear side of a large board placed vertically in such a position as to set up interference of the sound. When the air in the room was at rest, these positions of inter- ference were easily detected with a resonator. The case was analogous to the optical phe- nomenon where light is diffracted around a similar obstacle so as to produce interference. When the windows were opened to allow the cold winter air to pour in, and also when the registers were opened to admit currents of air at 100 deg. C, the phenomena of interference instantly disappeared. The experiment was re- pealed many times, always with the same re- sult. Experiments by the author confirm this re- sult described by Jacques: In a laboratory about 25 ft. square a whistle was blown, while a receiver a Rayleigh suspended disc was placed across the room and responded to the sound. Small air currents caused a difference in the deflections, while a draft from a window through the door made large fluctuations in the readings. Steady deflections were almost impossible to obtain with air currents in the room. FURTHER EXPERIMENTS BY JACQUES In this same connection Jacques performed another experiment. He set up conditions analogous to Tyndall's experiment (see Fig. i ), so as to approximate the state of affairs in an auditorium. Thus, at places marked -f- ne placed "substances heated to such tempera- tures as to give rise to currents of air cor- responding in density to those found in an auditorium. At A was placed a source of sound, being in some cases an organ pipe, in others a man who spoke in a clear and distinct voice, and in others various musical instru- ments on which simple combinations of notes were played. At B was placed the ear, . . . the best instrument imaginable for determin- ing the qualities of the sounds." The experi- ments showed that the clear notes of the or- gan pipe lost not only decidedly in intensity but also in distinctness. The effect on the man's voice was to decrease the intensity, and also to make it slightly confused and indistinct, as if each syllable was repeated several times in very close succession. With a flute the ef- fect was the same as for a man's voice. The effect on a violin seemed to be considerably less. With a drum no effect whatever was observed. Jacques concludes: "Currents of air of varying density, then, cause, first, a de- crease in intensity of sound, and, second, an indistinctness or confusion of sound." Another instance of the same nature is men- tioned by Sabine (loc. cit.). In the House of Commons in 1835 " a current of hot air, rising in a broad sheet along the center of the house, reflected the sound passing from side to side and rendered the intonation indistinct. One of the members . . . stated that he had often noticed that he could not hear a member op- posite him distinctly at particular times unless he shifted his position along the bench, and on examining the place referred to it was found that he had moved to a position where the hot air current no longer passed between him and the member speaking." The conclusion to be drawn from Jacques' experiments is that haphazard currents in an auditorium are detrimental to the acoustics. It is not to be concluded that the other arrange- ment of the air current in one large stream will be of great benefit unless a very great dif- ference of temperature is set up between the heated current and the surrounding air. Jacques simply showed that such a stream had only a little effect in distorting the sound. Probably the acoustics were good without any ventilation, and it is to be regretted that Jacques records no experiments performed with the ventilation entirely cut off. Such an experiment would have shown whether the good acoustical properties were due to the arrangement of the ventilation or to the other features of the room. AUTHOR'S EXPERIMENTS The author has performed some experi- ments suggested by these conclusions to deter- mine whether or not heated air currents in a room cut down the duration of sound. Thus, if air currents reflect much sound they ought to act as reflectors, or extra partitions, and multiply the number of the reflections of the sound per second. Since a fraction of the energy of the sound waves is absorbed at each reflection, the presence of the air currents would decrease the duration of the sound. The experiment involved Sabine's well-known method ("American Architect," 1900), where the absorbing power of substances for sound may be determined by measuring the time of duration of the "residual sound" i. e., the sound that persists after the source of sound is stopped. In a room about 20 ft. square, cleared of all furniture, an organ pipe was sounded for several seconds and then stopped. The time taken for the sound to die out was noted by an observer, the record being made electrically on a chronograph drum. The ob- servation was repeated when two long rows of gas burners, placed on the floor, were lighted. In this case there were two sheets of hot gas to interfere with the progress of the sound. Further data were obtained with the gas flames extinguished; also, a fourth meas- urement with two windows open. The results follow, the figuring representing duration of the residual sound after the source of sound was stopped : (a) For room with bare walls 3-155 sec. (b) With burners lit 2.960 sec. (c) With two windows open 2.512 sec. It is seen that the effect is small, but in the right direction to confirm the theory. The ab- sorbing power of the gas currents is very small, since the two open windows with very much smaller area have a much greater effect. Hence, air currents in an auditorium cannot be expected to have any pronounced effect as absorbers of sound. MINOR FACTORS AFFECTING SOUND WAVES In order to complete the discussion of the effect of a current of air on the acoustics in an auditorium there should be considered sev- eral other factors of minor importance that may affect the progress of the sound waves namely, the presence of moisture in the air, the motion of the stream, and the effect of the carbon dioxide breathed out by the auditors. The presence of moisture would have but lit- tle effect on the sound waves, since it has al- ready been shown for the extreme case where the air in the stream is saturated with mois- ture and the surrounding air completely dry that the effect is small. Under usual condi- tions the air in the stream would not be satu- rated, neither would the air surrounding the auditors be completely dry; therefore, the ef- fect would be still smaller and may be disre- garded. The motion of the air can be shown "to have a negligible effect provided the velocity of the stream is not more than 60 cm. (about 2 ft.) per second. (See theory at end of paper.) This statement seems to contradict the well-known action of the wind whereby sounds may be heard a long distance from the source. For this case the action follows be- cause the wind may act on the sound for a long distance. Also, a high velocity of the wind may intensify the effect. Neither the condition of long distance action nor of high velocity is found in the usual air currents in an auditorium; hence the motion has a negligible effect. It should be pointed out that the theory de- veloped by Lord Rayleigh assumes certain re- strictions with which the conditions in an auditorium are at variance in some respects. Thus, the transition layer between the two media should be small compared with the wave length of the incident sound. If it be assumed that the wave lengths of ordinary sounds for women's voices range from 2 to 6 ft. and for men from 4 to 18 ft. (Winkelmann, "Hanclbuch der Physik," vol. 2, page 686), and further that the transition layer between warm and cold air has a thickness of i ft., it is seen that the theoretical condition is not fulfilled for the sounds of short-wave length. That is, reflection would take place fairly completely for the deep bass tones, but those of high pitch would be readily transmitted. The sounds ut- tered by a man would suffer more reflection than those by a woman; the notes of a bass viol would be more affected than the high notes of a violin. The theory also assumes the sound waves to be plane, whereas in an auditorium they are spherical as they come from a speaker. At some distance from the source the waves would become flatter, hence would accord more closely with the theory. CONCLUSIONS The previous discussion has shown both from theory and experiment that sound waves impinging on the boundary between two gases suffer reflection and refraction. The magni- tude of the effects depends chiefly on the dif- ference in density in the two gases. The differ- ence of density, in turn, depends on the differ- ence in temperature of the gases, or difference in moisture content, or because the two gases are different in nature Many of the common effects of gas currents on sound may be ex- plained by these considerations. It is shown that haphazard currents of air in an audi- torium make the hearing confused and indis- tinct. The principles evolved suggest certain ar- rangements in an auditorium that will help the acoustics. Hot stoves, radiators and hot air registers should be placed near the walls of the room so that no very hot currents of air be- come interposed between speaker and auditors (see Sabine, loc. cit). In theaters it would be an advantage to have footlights made up of incandescent lights instead of gas lamps, since the latter set up a sheet of hot gas between the players and the audience, with detriment to distinct hearing. The ventilation in an auditorium has practically no effect unless the currents are haphazard. For this case the sound becomes confused and indistinct. The best arrangement of the ventilation is to have it pass in steady streams with as few boundar- ies as possible, and with gentle motion so that no strong drafts are set up. It is not to be concluded that poor acoustics in an auditorium may be greatly improved by a ventilating sys- tem. What is to be concluded is that the acoustics may be made worse when the cur- rents of air are unsteady with many boun- daries between hot and cold layers. It is not without interest to apply the con- clusions brought forth to other systems of ven- tilation than the one described by Jacques. Conference with Prof. J. M. White, supervis- ing architect of the University of Illinois, has brought forth the following discussion: In order to ventilate an audience room the air must either be brought in through numer- ous openings in the floor at a low velocity and at a temperature of about 70 deg. Fahr., or it must be brought in at a higher temperature and velocity through wall registers. With the latter method it is difficult to bring the air down to the breathing zone. The case de- scribed by Jacques is of this type. It seems likely that the heated stream of fresh air passes over the heads of most of the audience and is breathed only by those in the upper gal- leries, where the air is drawn out. Such a cur- rent of warm air might be valuable as a heat- ing medium, because there is usually a large loss of heat through the roof of an audience room. Suppose the stream of air is not taken out at the roof but, after being cooled by con- tact with the upper surface and wall of the room, falls to the floor and is taken out by outlets so distributed as to give the greatest probability of its traveling across the breathing zone. For this case it would be of value both for heating and ventilating, but would give haphazard currents which would be detri- mental to good acoustics. Consider now the other method of ventila- tion. The warm air comes through the floor and, rising about the audience, is further heated and goes vertically to the outlets in the ceiling. Some of the warm air becomes cooled by contact with the cold walls and falls back to the floor, thus setting up haphazard cur- rents; the main effect is, however, to give a large stream of air of nearly uniform tempera- ture and velocity. Its effect on the sound would be small. In case the auditorium were in the center of the building and surrounded by warm rooms the effect on the sound would be still less, since there would be no descend- ing cold currents of air at the side walls. Considering all the circumstances, this last arrangement seems to be the best one for acoustics. As already pointed out, it would be more advantageous to have the uniform stream start from the stage and go with the sound; but this plan has greater disadvantages for the ventilation. Professor Sabine, from a some- what different line of reasoning, has come to the same conclusion namely, that the vertical stream of air is best for the acoustics (loc. cit.). Lord Rayleigh has developed the general re- lations whereby reflection and refraction of sound at the boundary of two media may be calculated. ("Theory of Sound," vol. 2, sec- tion 270.) Imagine two different gases, each homogeneous, lying one above the other so that the dividing plane is horizontal. (See Fig. 3.) A train of plane waves striking this boundary more or less obliquely will be partly reflected and partly transmitted, the transmitted por- tion being refracted. The equation applying to the case in hand follows from the general relations and reads : 9 Where 9" and 9' are the amplitudes respective- ly of the reflected and incident waves, V the velocity of sound in the medium of density p UfperMedium Density*p, Velocity^, that contains the incident waves, and V and p! the corresponding values for the other me- dium, 6 is the angle between the normal to the boundary plane and the direction of propaga- tion of the incident waves. REFLECTION OF SOUND From the equation may be calculated the ratio of the amplitude of the reflected wave to that of the incident wave; or, better still, the ratio of the energies, since the energy is pro- portional to the square of the amplitude. For perpendicular incidence at a surface be- tween air and hydrogen Lord Rayleigh has calculated that about one-third of the energy is reflected. Inspection of equation (i) shows that for perpendicular incidence = o, and tan 6 = 0, so that the relation reduces to This may be further simplified by using the relation for the velocity of sound in gases (3) where p is the pressure of the gas, ? the density and 8 the ratio of the specific heats. The ratio of the velocities for air and hydro- gen is since p has the same value for both gases at the boundary and 8 is the same (1.41) for air and hydrogen. The densities of air and hydro- gen are respectively 0.001276 and 0.00008837. Equation (i) may now be written 9"/Y = (i Vp/pJ -f- (i + = - (2.8/4.8) (4) The energy relation follows: (9'0 2 =(2.8/ 4 .8) 2 (9T = 0.34(9')'; that is, about one-third of the incident energy is reflected. For the case of two layers of air, one at o deg. C. and the other at 10 deg., only about 80/100,000 of the energy is reflected. Before calculating the temperature effect it is better to simplify equation (2). This may be done by taking VJV = VP/Pi an d using the relation for the change in density with the tempera- ture : p/p t = i -f~ 0.00366 1, where p is the density at o deg. and ^ the density at t deg. C. above zero. Equation (2) becomes: 9" i V J 0.00366 t 9' i -f- V I + 0.00366 t (5) For t = 10 deg., 9"/V = 0.0089, an d the ratio of the energies, (9")Y(/p -f- M 2 /2 + U = /> /po + M 2 /2 + Uo where p is the pressure in a stream of fluid, p the density, and u the velocity, and U the internal energy. For gases such as air, oxygen, etc., U = c v T with sufficient exactness, where c v is the specific heat for constant volume and T is the absolute temperature. By using also the relation for gases pv = RT, or />/p = RT, Bernoulli's equation becomes t> U . C v p 1 = P 2 flp c v p or since it may be shown that R = c p c v , where c p is the specific heat for constant pres- sure. Substituting 8 = c p /c v in the relation F 2 = 8/>/p, where V is the velocity of sound, there is obtained 8-1 i i Applying this equation to the moving stream of air, the left-hand side of the equation may refer to a point in the stream where the velocity is u and the right-hand side to any other point. For this other point choose a place where the velocity is practically zero i. e., where V is the velocity of sound in air at rest. The equation becomes _ 2 ~ : 8 from which the ratio V/V may be calculated if u is given. This ratio, V/V , may be thought of as the ratio of the velocity of sound in the stream to the velocity of sound outside the stream, since the air outside the stream is at rest. Assuming u = 60 cm per second and V = 34,500 cm per second, V is calculated to be 34,499 cm per second; that is, practically the same as V . Therefore, prac- tically no reflection would occur at the boun- dary of a moving stream of air, since V/V is practically equal to unity, and substitution in equation ( i ) would give 9"/V = i- e -> no reflection. CONDITIONS OF SENSIBILITY OF PHOTO-ELECTRIC CELLS WITH ALKALI METALS AND HYDROGEN. BY J. G. KEMP. [Reprinted from the PHYSICAL REVIEW, N.S., Vol. I., No. 4, April, 1913.] CONDITIONS OF SENSIBILITY OF PHOTO-ELECTRIC CELLS WITH ALKALI METALS AND HYDROGEN. BY J. G. KEMP. THE object of this investigation is a systematic quantitative study of the conditions of sensibility of photo-electric cells of alkali metals with hydrogen and a determination of the work required to draw an electron out of an atom. The photo-electric phenomena are very important in connection with the theory of radiation, and for photometric purposes. Planck's theory of radiation requires that the potential due to incident light should in- crease proportional to the frequency of the light. Moreover, if the theory of the units of energy strikes reality, we should expect that the photo-electric current for very weak intensities of light becomes inter- mittent, as the electrons are given out only from time to time, so that the phenomenon should resemble the radioactive scintillator. If the intensity of the incident light falls below a critical value, an electron can only escape from the metal, if its kinetic energy is at least equal to the unit of energy received from the beam of light. Photometric measure- ments have already been carried out by Elster and Geitel, by Richtmeier, 1 by E. L. Nichols and E. Merritt. 2 As the sensitiveness of the photo- electric cells is very great, comparable indeed with the sensitiveness of the selenium cell, we hope to use these photo-electric cells for the measure- ment of the light from the fixed stars. The sensitiveness of the photo-electric cells has been increased con- siderably by the formation of an alkalihydride and by replacing hydrogen by helium. This has been done by Elster and Geitel. 3 The work necessary to produce an ion can be determined by two inde- pendent methods. One method is based on the ionization by a particles, the other on the potential difference which in a discharge tube is necessary to produce ionization by collision. The results of the two methods do not satisfactorily agree with each other. A larger number of determinations of this quantity is necessary before we can explain the difference of the results. 1 PHYSICAL REVIEW, 29, p. 71, 1909. * PHYSICAL REVIEW, 34, p. 475, 1912. 1 Physik. Zeitschrift, n, April, 1910, and August, 1911. 'Iron ffiny $4!'] SENSIBILITY OF PHOTO-ELECTRIC CELLS. 2J$ DESCRIPTION OF APPARATUS. It was required to find the sensitiveness of the photo-electric cells as function of the gas pressure, the electrode distance, the area of metal illuminated, the voltage applied to the electrodes and the intensity of illumination. Fig. I shows the glass tube used in making the cell. A spherical bulb, 2.5 cm. in diameter, has two tubes i.o cm. in diameter, sealed horizontally and diametrically oppo- site each other. A vertical tube, 1.8 cm. in diameter, about 15 cm. long is sealed in the top of the bulb. At the top of this vertical tube a plati- num wire is sealed and fused to an alumi- num rod 0.4 cm. in diameter and 10 cm. in length. To the lower end of the aluminum rod is attached a brass spiral spring to which is connected the platinum wire an- f ^ ode. The anode, a, being sealed through Q \ ^ , -A the lower end of the glass tube which tele- ^3-^ scopes the aluminum rod. At the upper end Fig j of this glass tube is attached an iron ring which fits neatly inside the larger tube. By means of an electromagnet, using a current of 2 amperes, the inner tube carrying the anode, a, can be held in any desired position relative to the cathode, c, at the bottom of the bulb. At the bottom of the bulb and diametrically opposite the anode, a, is sealed the cathode, c, the upper point of which does not extend beyond the surface of the inside of the bulb. In some of the cells the inside of the lower surface of the bulb was silvered, the metal distilled into it and deposited upon the mirror surface. In this way a good contact was insured between the platinum and the metal. In some of the tubes the metal was not distilled into the bulb but poured into it while in the molten state and allowed to solidify over the platinum electrode. The metal in all cases was used as the cathode of the cell. In order to form the sensitive hydride the alkali metal, that is, the cathode, was connected to the negative terminal of a battery of 300 or 400 volts while a resistance of 3,000 ohms and a galvanometer was placed in series with the positive terminal of battery and the anode of the cell. The pressure of the hydrogen gas in the cell was then reduced until the current flowing between anode and cathode caused a faint glow to fill the whole tube. The metal surface, which was very bright before the illumination ap- peared in the tube, afterward became colored, being brownish for sodium, 276 J. G. KEMP. [SECOND [SERIES. bluish violet for potassium, and light greenish for rubidium and caesium. These colors are due to the formation of a compound of the hydrogen and the metal, which is called a hydride. When the hydrogen is replaced by argon or helium, the cell maintains its high sensitiveness constant for a long time. And even if the metal remains in contact with hydrogen, the sensitiveness did not seem to change during the few days in which the readings were taken. The distance between the electrodes could be changed by means of an electromagnet, arranged inside the light-tight box, and a cathetom- eter was used for the accurate determination of the electrode distance. Fig. 2 shows the entire arrangement of the apparatus for the investi- gation. The photo-electric cell is enclosed in a light-tight box. Wires connected to the anode and cathode, and to the electromagnet, M, pass forth Fig. 2. through insulators in the walls of the box. The cell is sealed to the system containing a Macleod gauge for measuring pressures up to 0.24 cm., a closed manometer for measuring the higher pressures, a regulator for obtaining small variations in pressure, a tube containing palladium metal strips for supplying pure hydrogen gas, and an air pump The palladium metal was charged with hydrogen gas by the electrolytic method. With an electrolyte of one part of H 2 SO4 and three parts of H 2 O, the anode being platinum, and the palladium metal the cathode, hydrogen gas was absorbed by the cathode when 2.5 volts was connected across the electrodes. After charging the palladium, the tube containing it was sealed to the system. When the tube is heated with a small bunsen flame, the metal gives off pure hydrogen gas. The whole glass system, when the pump was cut off, could be filled to a pressure of about 25 cm. when the palladium was heated. " 4 '] SENSIBILITY OF PHOTO-ELECTRIC CELLS. The galvanometer used is a Leeds and Northrup type HS, the sensi- bility being 3.78 X io~ 10 amp. per mm. Deflection for 2 meters scale distance. The anode of the cell was connected to the earth through the galvanometer and a megohm resistance. The cathode of the cell was connected to a variable point in a water rheostat which is in series with about 640 volts from a storage battery. The voltage applied to cathode could be varied by means of the water rheostat and it was measured by a Kelvin electrostatic voltmeter reading 0-600 volts. The variation of the area of the metal illuminated was obtained by varying the opening of the iris diaphragm A, which is placed at the lower end of a brass tube. This tube was blackened on the inside to prevent reflection of light. By moving the lamp on the guide the intensity of illumination on the metal in the photo-electric cell could be varied, and this variation calculated directly by means of the inverse square law. METHOD. Since the most sensitive conditions for the photo-electric effect are being sought, it is necessary to study the effect due to varying all the possible conditions in order to find the most effective set of conditions. The variables in this work are the following: P the pressure of the gas, D the distance between the electrodes, V the potential difference applied to electrodes, A the area of metal illuminated, L the intensity of illumina- tion, t the temperature of the cell, and d the galvanometer deflection which is proportional to the current. Two sets of readings are possible for each cell, namely, before forming and after forming the hydride surface. In this paper this process will be called forming. Four cells were studied: one with caesium and three with potassium metal. The readings were taken in the order as follows: With /, Z,, A, P and D constant the values of the deflections, d, of the galvanometer were read for increasing values of V. Thus values of current and voltage were obtained for an ionization curve. This was repeated for three and in some cases four distances of D. From the above data four ionization curves are obtained which show the effect of varying the distance between the electrodes for constant values of /, L, A and P. If the above three or four ionization curves be called a set, then it is possible to get as many sets as there are values of P, the gas pressure. From three to five different values of P were selected for each cell and in this way the effect due to change of pressure was studied. J.G. KEMP. [fg; lonizatioh curves were also obtained in which A, L, P and D are constant for three or four different temperatures. After the forming process similar sets of ionization curves were taken except those for temperature changes. In addition to the ionization curves taken after forming the cell No. 4, sets of data were taken in which L, F, P, I and D are constant while A and the current varied. Also readings were taken for A, V, P, t and D constant while L and the current varied. A total of thirty-six plates, each containing four or five curves were obtained for the four cells. On account of the similarity of the large number of curves and data taken only representative curves will be given for potassium cell number four. CURVES. A in cm 2 , represents the area of metal illuminated. L in candle feet represents the intensity of illumination. t in C. the temperature of the cell. P in mm. mercury represents the pressure of the hydrogen gas. D in cm. represents the distance between the electrodes. F in volts represents the potential difference between electrodes. d in mm. represents the galvanometer deflections. CRITICAL VOLTAGE AND CURRENT. It was found that when the voltage was applied to the cells, it could be increased to a certain definite maximum value before a deflection of the galvanometer was noticeable when the light was not acting. If this voltage was exceeded by an amount hardly readable on the voltmeter a deflection of the galvanometer resulted. Furthermore, if the light was permitted to act and the voltage applied, equal to the maximum value determined as stated above, a definite deflection of the galvanometer was produced; and, when the light was suddenly turned off the galvanometer deflection always became zero. However, if this maximum value of the voltage were exceeded and the light turned off, the deflection of the galvanometer was decreased but never became zero. This voltage, therefore, represents the maximum which may be applied to the cell, in this particular case, and at the same time have the ionization current produced only by the action of light. This value of the voltage I shall call the "critical voltage," and the corresponding current the "critical current" for this particular condition of the photo-electric cell. The critical voltage and the critical current taken together give a definite criterion for determining the best conditions for sensitiveness. When the critical current is a maximum and the critical voltage is a VOL. I No. 4. SENSIBILITY OF PHOTO-ELECTRIC CELLS. 279 minimum, then the most sensitive conditions obtain. Therefore, the critical voltage and the critical current are given in the data and shown by the vertical lines as for example ab in Fig. 3. If the voltage is increased beyond the critical value, when the cell is in the dark, the current will increase suddenly, so that it cannot be measured with the galvanometer. This indicates that the sparking voltage is not much greater than the critical voltage. Some phys- m . " ical results, chosen from a large .| ^ number of observations are given J! 3" fr. t in Figs. 3 to 17. Four groups of curves will be given. In the first group, Figs. 3 to 10, relating to a potassium cell before forma- tion of the hydride, the two most important independent va- riables, the electrode distance and the gas pressure are studied. The same holds for the second group of curves, Figs. 11-15, which however have been taken after the formation of the hy- dride. The variation of the area illuminated is represented in Fig. 16, and the variation of the intensity of illumination in Fig. 17. Voltage on Metal. Variation of electrode distance reading'from left to right 0.5-1-2-3 cm. Gas pressure 5 mm. Before forming. - Fig. 3. to \ H w i v 1* Q m u C Q \ OIQ / 1 / 7 I O ^ 3 . o -1 Voltage on Metal. Variation of electrode distance reading from left to right 0.5-1-2-3 cm. Gas pressure 2 mm. Before forming. A = 4.36 cm'. L - 0.22 C.f. / = 26 C. Fig. 4. The following remarks may be made on curves Figs. 3-10. The illuminating voltages are in the order of the values of D. 280 J. G. KEMP. \ SECOND [SERIES. Fig. 3. The critical voltage for D = 0.5 cm. is the smallest, while the critical current for D = i.o cm. is the largest; therefore, the best condi- tion for this pressure is for some value of D between I and 2 cm. 60 Jsc 19O *Ml 260 000 J40 Voltage on Metal. Variation of electrode distance read- ing from left to right 1-0.5-2-3 cm. Gas pressure 1 mm. Before forming. A - 4.36 cm. L = 0.22 C.f. 7 = 26 C. Fig. 5. soo s o Voltage on Metal. Variation of electrode distance reading from left to right 0.5-1-2-3 cm. Temp, salt and ice bath. Gas pressure 3 mm. Be- fore forming. A = 4.36 cm 2 . L = 0.22 C.f. t = 20 C. Fig. 6. Fig. 4. The order of the illuminating voltages is the same as that for values of D. The critical voltage for D = 0.5 cm. is the smallest and the critical current is the largest; therefore, the best conditions for sensitiveness are shown by this curve. Fig. 5. The order of the illuminating voltages is not the same as that Voltage on Metal. Variation of electrode distance reading from left to right 0.5-1-2-3 cm. Temp. C. Gas pressure 3 mm. Before forming. A = 4.36 cm 2 . L = 0.22 C.f. t C. Fig. 7. VOL. I.I ).4. J No. SENSIBILITY OF PHOTO-ELECTRIC CELLS. 28l for values of D. The curve for D 0.5 cm. lies between curves for D = i.o cm. and D = 2.0 cm. The curve D = i.o cm. shows best conditions for sensitiveness. ~SOO sic Voltage on Metal. Variation of electrode distance reading from left to right 0,5-1-2-3 cm. Temp. 38 C. Gas pressure 3 mm. Before forming. A = 4.36 cm 2 . L = 0.22 C.f. t - 38 C. Fig. 8. Fig. 6. The order of the illuminating voltages is regular. The con- ditions of sensitiveness are much better as represented in curve for D = 2.0 cm. . <* 2 * "3 so .2 $ ^ * IT* . rt 20 > H . I i j 2 2 I 1 f ^J E xX ^ ^-^ / # ? 10 1 80 J. y j< (7 4 4 40 41 w A ^o 3 * J J ^ 00 Voltage on Metal. Variation of gas pressure reading from left to right 2- 1-3-5-8 mm. Electrode distance 1 cm. Before form- ing. A = 4.36 cm*. L = 0.22 C.f. Fig. 9. Voltage on Metal. Variation of gas pressure read- ing from left to right 2-3-1-5-8 mm. Electrode distance 0. 5 cm. Before forming. A = 4.36 cm 1 . L = 0.22 C.f. Fig. 10. Fig. 7. The order of the illuminating voltages is regular. The best conditions of sensitiveness are represented by a curve that would lie between curves for D = 0.5 cm. and D = i.o cm. 282 J. G. KEMP. [SECOND [SERIES. Fig. 8. The order of the illuminating voltages is regular. The best conditions for sensitiveness are represented by a curve which will lie between curves for D = i.o cm. and D = 2.0 cm. Voltage on Metal. Variation of electrode distance reading from left to right 0.5-1-2 cm. Gas pressure 10 mm. After forming. A = 4.36 cm 2 . L = 0.22 C.f. t = 24 C. Fig. 11. Fig. 9. The curve for P = i.o mm. lies between curves P = 2.0 mm. and P = 3.0 mm., showing that the critical pressure for minimum illuminating voltage is in the region of 2 mm. The best conditions of sensitiveness are represented by a curve which lies between curves for P = 3.0 mm. and P = 5.0 mm. . KO % * \ 1 Q w 1 | i 1 r O 20 1 1 I i j / f\ 2 J ^ , ^ ' _--< * C^ _^ gj . ' -^ I c< J9O i \O a o 3/O 3SO 390 4 9 t> s/o Voltage on Metal. Variation of electrode distance reading from left to right. 0.5-1-2-3 cm. Gas pressure 3 mm. After forming. A = 4.36 cm'. L = 0.22 C.f. t = 25 C. Fig. 12. Fig. 10. The curve for P = i.o mm. lies between curves for P = 3.0 mm. and P = 5.0 mm. This indicates that the critical pressure at VOL. I.I No. 4. J SENSIBILITY OF PHOTO-ELECTRIC CELLS. which the illuminating voltage is a minimum lies in the region of P = 2.0 mm. The best conditions for sensitiveness are represented by a curve which lies between curves for pressure between 2 and 3 mm. . Voltage on Metal. Variation of electrode distance reading from left to right 0.5-1-2-3 cm After forming. A = 4.36 cm 2 . L = 0.22 C.f. Fig. 13. Gas pressure 2 mm, 26 C. The next set of figures, n to 15, represent values observed after the formation of the hydride. The following notes may be made. Fig. II. The order of illuminating voltages is regular. The best conditions for sensitiveness are shown by curve for D = 0.5 cm. Voltage on Metal. Variation of gas pressure reading from left to right 1-2-3-5-10 mm. Electrode distance 1 cm. After forming. A = 4.36 cm 2 . L = 0.22 C.f. Fig. 14. Fig. 12. The order of illuminating voltages is regular. The best conditions for sensitiveness are shown by curve for D = 0.5 cm. Fig. 13. The order of illuminating voltages is regular. The best conditions for sensitiveness are shown by a curve which lies between curves for D = 0.5 cm. and D i.o cm. 284 J. G. KEMP. [SECOND [SERIES. Fig. 14. These curves show conditions of sensitiveness for different pressures and D = i.o cm. The curve representing best conditions for sensitiveness lies near the curve for P = 3.0 mm. Voltage on Metal. Variation of pressure reading from left to right 2-1-3-5-10 mm. Electrode distance 0.5 cm. After forming. A 4.36 cm 2 . L = 0.22 C.f. Fig. 15. Fig. 15. The curves show the conditions for sensitiveness for different pressures and D = 0.5 cm. The curve representing best conditions for sensitiveness lies near the curve for P = 3.0 mm. o * Area of Metal Illuminated. Variation of area of metal illuminated. Intensity of illumination 0.22 C.f. Gas pressure 2 mm. Electrode distance 0.5 cm. Voltage on metal reading from top downward 295, 294, 293 volts. Fig. 16. The curves of Fig. 16 show the variation of area of metal illuminated. The form of these curves indicates that variations in small areas illumi- VOL. Li No. 4. J SENSIBILITY OF PHOTO-ELECTRIC CELLS. 285 nated produce large changes in the current, and variations in large areas illuminated produce small changes in the current. These facts show that there is a maximum area of illumination for this particular type of photo-electric cell which, if exceeded, will not increase the sensitiveness. The form of the curve should be a straight line if the electric field were uniform, the surface conditions uniform, with no reflection of the light, and no shadow caused by the electrode. In this cell the above conditions were not fulfilled, therefore the form of the curve is not a straight line. It follows finally a system of curves showing the variation of the intensity of illumination for three different voltages, the observa- Intensity of Illumination = .K/P. Variation of intensity of illumination. Electrode distance 0.5 cm. Voltage on metal reading from top downward 366, 365, 364 volts. After forming. Fig. 17. tions are taken after the forming of the cell. In Fig. 17 showing variation of current with intensity of illumination for P = 5 mm. the points for the smaller voltages lie more nearly on a straight line. The largest error in the intensity for the point farthest from the line is 7 per cent, of .15 C.f. or .01 C.f. The points for smaller intensities show much smaller deviations than those for larger intensities. The higher voltages applied caused unsteadiness of the current, hence, the galvanometer deflections are liable to larger errors. BEST CONDITIONS FOR SENSITIVENESS. By comparing the values for the critical voltages and currents ob- tained from the curves the best sensitive conditions may be selected. A table of these values is given below for both before and after forming the hydride on the surface of the metal. 286 J. G. KEMP. f SECOND L SERIES. TABLE TO SHOW BEST CONDITIONS FOR SENSITIVENESS. V = critical voltage. / = critical current in galvanometer deflections. D best distance between electrodes in cms. P = best pressure in mm. Before Forming Metal. Figure. V / D p 3 460 to 527 16 to 28 1 to 2 5.0 4 304 26 0.5 2.0 5 349 to 366 6 to 9 1 to 2 1.0 6 454 8 2 3 1 7 335 to 396 10 to 45 0.5 to 1.0 3 2 8 383 to 431 7 to 11 1 to 2 3 3 9 387 to 460 28 to 29 1 3 to 5 10 304 to 324 26 to 32 0.5 2 to 3 After Forming Metal. 11 479 280 0.5 10 12 331 off scale 0.5 3 13 296 to 331 123 to 190 0.5 to 1.0 2 14 374 203 1 3 15 331 off scale 0.5 3 By inspection of the table above, it is seen that the best conditions for sensitiveness before forming are about V = 300 volts. D = 0.5 cm. P = 2 to 3 mm. / = 25 C. And the best conditions for sensitiveness after forming are about V = 330 volts. D = 0.5 cm. P = 3 mm. / = 25 C. The cell is about 100 times more sensitive after forming than before forming. THEORETICAL DEDUCTION OF MEASUREMENT OF INTENSITY OF ILLUMINATION. If the intensity of illumination varies directly with the current for very small intensities, then it is possible to calculate the intensity meas- urable with an instrument of given sensibility. 1 About 20 C. salt and ice. 2 C. 38 C. No" 4 L ] SENSIBILITY OF PHOTO-ELECTRIC CELLS. 287 From Fig. 18 below it is seen that for the curve of 366 volts, d 130 tan 6 = - = - - = 0.65, 5 200 or d S = tan 6 0.65 Fig. 18. cd I current flowing, c = 3.78 X IO" 10 amp. per mm. deflection, d = 0.65 X 3-78 X i^i mm " but K and for particular values of 5 = 200, and I 2 (100 cm.) 2 , K = SI 2 = 200 X (ioo) 2 cm. = 2 X io 6 cm. S = , or / Substitute value of 2JX I0<5 _ 7 = {2 X io 6 \ 5 5 = 0.65 X 378 X io- 10 in eq. above, then |2X io 6 X 0.65 X 3.78 X IP" 10 _ f 4.9 X io~ 4 = \ I = \ ~T By means of an electrometer a current / = io~ 12 can be measured. Substituting this value of I in the equation above, then, -4 4.9 X io- 4 =12 = 2 - 21 * io 4 cm. or 221 meters, the distance the 2.47 c.p. lamp could be removed from the cell and still be detected. By means of a tilted electroscope a current / = io~ 15 amperes can be measured. Substitute this value in the equation, = \ 15 ^4-9 X IQl1 = 7 X io 5 cm. or 7 kilometers or 4.3 miles. The 2.47 c.p. lamp could be detected by means of an electroscope at a distance of 4.3 miles. To detect a candle instead of the 2.47 c.p. lamp at 4.3 miles distance by means of the tilted electroscope of io~ 15 sensi- bility the distance could be as follows : Since the intensities of illumination of cell must be the same, then, 288 J. G. KEMP. [SERIES. (4-3) 2 'P ' v< 47 Professor Joel Stebbins, 1 of the University of Illinois, in his work on measuring the variation of intensity of illumination of the variable stars Algol and others used a selenium cell. It is possible to detect a candle at a distance of 500 meters, or 0.3 mile, with such a selenium cell. The equation for the distance at which this potassium cell is sensitive when the current is measured with a tilted electroscope is and for some other distance it is k m = V7 2 ' /I 2 /2 yr = , /i = 7 X io 5 cm., k = 5 X io 4 cm., then /! 2 49 X io 10 v = 25 x io 8 ==2X a pp roximatel y- Thus it is seen that the potassium cell is about two hundred times more sensitive than the selenium cell. ENERGY REQUIRED TO PRODUCE AN ION. To produce an ion a certain minimum amount of energy is required. This energy is that required to draw an electron out of an isolated mole- cule against the force of attraction of the positive charge of the molecule. Let Ri be the radius of the molecule, e\, the positive charge, e 2 , the negative charge of electron. If the electron be displaced a distance dR the work done will be **-%**. The total energy required to draw an electron outside of the influence of the positive charge is W = I -fa dR = -jr- units of work. ei = e 2 = 4.67 X io- 10 E.S.U. R l io~ 8 cm. for hydrogen. 1 Astrophysical Journal, October, 1911. SENSIBILITY OF PHOTO-ELECTRIC CELLS. 289 the minimum amount of energy required to draw an electron from an isolated molecule of hydrogen or to produce a hydrogen ion. For an isolated molecule it is necessary to withdraw the electron to an infinite distance from the center. If the molecule, however, is in an electric field the force of attraction between the molecule and the electron is zero at a distance say R% from the center. The effect of the electric field tends to decrease the energy required to withdraw the electron on one side of the molecule (with references to the direction of external electric field) while that on the opposite side is increased. Let Fig. 19 represent the molecule of radius Rii H is the direction of the external field in the direction of motion, Oa, of the electron. Let Rz be the distance beyond which the electric attraction between the positive charge of the molecule and the electron is zero, The work required to withdraw the electron beyond the influ- Fig. 19. ence of the molecule is W = J -j^dR = but e\ ei = e\ and it is reasonable to assume Substituting the values for R\ and e, W ==**= -urx --.P. Thus the value of W in calculation (2) is three fourths that in calcula- tion (i). Hence 2.18 X icr 11 ergs is not the minimum value. The minimum amount of energy required to produce an ion by col- lision can be determined roughly from the data taken in this investigation. For the conditions of this work the minimum energy is W = Eel, where E is the potential gradient, or electric force, e is the charge of a negative ion or electron, and / is the mean free path of an ion. The force E can be determined roughly as follows: The voltage applied to the electrodes of the cell necessary to produce velocities high enough to cause ionization by collision, is obtained from the ionization curves. This voltage is shown very distinctly at the point on the curve where the ordinate or current shows an increase after the saturation state has been reached. Let V be this voltage taken from the curve, and let D be the distance between the electrodes. Then, 3Qp> . E= mE .S.U. 290 J. G. KEMP. (a) FIRST ASSUMPTION REGARDING MEAN FREE PATH OF ELECTRONS. Assuming that the negative ions or electrons and the molecules of the hydrogen gas act as a mixture of two gases, the equation of the mean free path given by Maxwell in the kinetic theory of gases is h- r .' .. / YYl\ ^> YHz for the electrons, for hydrogen molecules. For an electron an the diameter of the sphere of action when two elec- trons collide is practically zero. But cri 2 the diameter of the sphere of action when an electron collides with a molecule of hydrogen is assumed equal to the radius of the molecule or icr 8 cm. m\ is the mass of an electron equal to 8.8 X io~ 28 grams. mz is the mass of a hydrogen molecule equal to 1.6 X io~ 24 grams. mi 8.8 X io~ 28 1.6 X io~ : 24 5.5 X io~ 4 gram This value is negligible in comparison with unity or ^1 I -\ -- 1 . The equation for the mean free path of the electron is n = M i) cm. In this equation Nz is the number of molecules per cubic centimeter. From the kinetic theory of gases Nz may be calculated. PV = RT, the gas law, which becomes PV = \L \N' = $mC 2 . Where L is the average total kinetic energy. N f is the number of molecules in volume V. C 2 is the square of average velocities of molecules. ^mC z = aT, where a is the universal constant. PV = %N'aT, or P = %NaT for unit volume. N = ^-PjaT the number of molecules per unit volume 3 13.6 X 980^ = 2T^T^r ;/zlsmcm - Suppose T = 27 + 273 = 300 for this work. VOL.^I.] SENSIBILITY OF PHOTO-ELECTRIC CELLS. 29 1 Substitute this value for N* in the expression for the mean free path. I _ 965 X IP" 5 T X 33 X io 16 fc X io- 16 " h Applying the equation W = Eel, e = 4.67 X io- 10 E.S.U. E = - - E.S.U. 30o l = 965 X io- 5 For h = 0.5 cm., D = i.o cm., V = 330 volts, 4.67 X io- 10 X 965 X io- 5 W = - - = 1.09 X io~ u ergs. 300 X i.o X 0.5 An average of ten determinations gave 1.05 X io~ u ergs for the minimum energy required to produce an ion in hydrogen by collision. (b) SECOND ASSUMPTION REGARDING MEAN FREE PATH OF ELECTRONS. If it be assumed that the negative ions or electrons occupy no space in the gas, or, that the hydrogen gas acts as though the electrons were not present, then the value of the mean free path is the same as that of the molecules. That is, 685 X I O- 5 4 - h - - cm. For h = 0.5 cm., D = i.o cm., V = 330 volts, 4.67 X io- 10 X 685 X IP" 5 X 330 W : 300 X 0.5 - - ' 7 X About 35 per cent, decrease from 1.05 X io~ 11 ergs. (c) THIRD ASSUMPTION REGARDING MEAN FREE PATH OF ELECTRONS. By using the assumption that the mean free path of the electrons is 4^/2 times mean free path of the hydrogen molecules, as Bishop 1 did, the following results are obtained. , /- ^42 i,36oXiQ- 5 = 4 v/2/ 2 - T33 x IQ _ 16A x 4 w , IJTjOcgLX 1,360 X io- 5 V ' IQ _ 15 V 300 Dh Dh 1 PHYSICAL REVIEW, 325, November, 1911. 2 9 2 J - G - KEMP. For P = 0.3 cm., D = i.o cm., V = 260 volts, 260 W = 21 X io~ 15 = 1.82 X io- n ergs. I X 0.3 An average of 10 calculations gives 1.77 X io~ u ergs. To recapitulate, the values determined above and those by other investigators are: 1. For an isolated molecule the theoretical value is 2.18 X io~ u ergs. 2. For a molecule in an electric field the theoretical value is 1 .63 X io~ n ergs. 3. The average of ten values determined from the data in accordance with the first assumption is 1.05 X io~~ n ergs. 4. The value determined in accordance with the second assumption is 0.70 X io~ n ergs. 5. The average of ten values determined in accordance with the third assumption is 1.77 X io~ u ergs. 6. Bishop obtained a value, by a method similar to that used in this work and in accordance with the third assumption used in the fifth determination, 1.58 X io~ u ergs. 7. Rutherford 1 determined the energy required to produce an ion by the alpha particle. His value is 2.7 X io~ n ergs. 8. Geiger, 2 and later Taylor, 3 using the same method, obtained about 5 X io~ 11 ergs, and other investigators obtained values even as large as 10 X io~ u ergs. In the method, based on the ionizing power of alpha particles, it is assumed that their loss of kinetic energy is entirely transformed into energy of ionization, and that the decrease of the kinetic energy over a certain range divided by the total numbers of ions produced gives the energy required to produce one ion. Since a part of the kinetic energy of the alpha particle increases the average kinetic energy of the gas without producing ions, the ionizing energy is taken too large and the energy required to produce an ion is necessarily too large. Value number (i) represents the minimum energy required to produce an ion when a molecule is isolated. This value is much larger than that for a molecule in an electric field. Rutherford's 4 determination is much nearer the value number (i) than any of the others. Bishop's determination is very close to the value number (2), while my determination of the ionizing energy is slightly larger. Since the assump- tion regarding the mean free path in numbers 5 and 6 are the same, and 1 Radio-Activity, second edition, p. 552. 1 Proc. Royal Soc., Vol. 82, p. 486, 1909. 8 Phil. Mag., p. 670, April, 1912. 4 Radio-Activity, second edition, p. 552. Na' 4 L ] SENSIBILITY OF PHOTO-ELECTRIC CELLS. 293 these values differ very slightly from the theoretical value number (2), it indicates that the assumptions made are not far from the truth. Owing to lack of time and space an exact determination of the minimum energy required to produce an ion by collision is impossible; in the near future, however, it is hoped that this can be done with the data already in hand. A design has been made for a sensitive photo-electric cell for photo- metric work in astronomy. It is expected to get a cell which will be sensitive enough to use instead of the erratic selenium cell now used. SUMMARY AND CONCLUSIONS. The following facts are established by this investigation for this type of photo-electric cell. 1. Owing to the low melting temperature of caesium the use of this metal in photo-electric cells for photometric use is very impractical. 2. The temperature at which it is best to operate a potassium cell is about 25 C. 3. Cooling the potassium cell much below 25 C. does not increase its sensitiveness. 4. The sensibility of a potassium cell can be increased more than 100 times by the process of forming the hydride surface. 5. The distance between the electrodes for best sensitiveness is about 0.5 cm. 6. The hydrogen gas pressure at which the cell is most sensitive lies between 2 and 3 mm. of mercury. 7. The potential difference applied to the electrodes for most sensitive conditions is about 330 volts. 8. The minimum energy required to produce an ion by collision was calculated from the data and found to be of the order 1.77 X io~ u ergs, while the theoretical value determined is 1.63 X io~ n ergs. 9. Assuming that the straight lines obtained which show the relation between current and intensity of illumination hold for exceedingly small intensities, then by using a tilted electroscope of sensibility io~ 15 amperes, a candle could be detected at a distance of 2.7 miles. This indicates that it is highly probable that a photo-electric cell could be used in astro- photometric work. The author takes great pleasure in acknowledging his indebtedness to Professor A. P. Carman for the facilities for this investigation, and to Professor Jakob Kunz, both for his general supervision of the work and for many valuable suggestions. LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS. The Use of Sounding-Boards in an Auditorium Reprinted from The Brickbuilde* June, 1913 The Use of Sounding-Boards in an Auditorium. BY F. R. WATSON. Assistant Professor of Physics, University of Illinois. OOUNDING-BOARDS are well O known because of their use in audi- ence halls where the acoustical proper- ties are unsatisfactory. Thus many churches are found equipped with this device with the expectation that the acoustics will be made better. Because of this common use the author has been led to test sounding-boards of different forms, to determine, if possible, their value in bettering- the acoustics of an auditorium. The experiments were carried out as a part of a more complete investigation of the acoustical properties of the audi- torium of the University of Illinois. This auditorium is shaped nearly like a hemisphere with several large arches and recesses to break the regularity of the inner surface. (See Figs. I and IV.) The original plans of the archi- tect were curtailed because the amount of money appropriated for the construc- tion of the building was insufficient for the purpose. The interior of the hall was built absolutely plain with no break- ing up of the smooth wall surfaces, and no furnishings were provided in the shape of carpets or curtains. The acoustical properties proved to be unsat- isfactory. A reverberation, or undue prolongation of the sound, existed. In addition, echoes are set up because of the large size of the room and because of the position and form of the walls. A diagnosis of the acoustics was made. The time of reverberation was deter- mined by Sabine's method* to be a little more than six seconds. The echoes were located by tracing out the paths taken by the sound. This was done by means of an arc-light backed by a parabolic reflector. t The arc gave out sound waves in addition to the light ; the two sets of waves traveling together, so that by noting where the light struck a wall, an observer could ' ' see ' ' where the sound traveled. The echoes were finally eliminated by placing canvas curtains so as to break up the sound waves that produced the trouble. It occurred to the author during the course of the investigation that sound- ing-boards might be helpful in curing the echoes. Several forms of boards were used. A flat board, about 5 feet square, inclined at an angle above the head of the speaker, produced but little effect. A canvas sheet, about 12 by 20 feet, similarly placed, was also unsatis- factory, although speakers said they could talk better under it than out in the open. Sounding-boards were then'used of a parabolic shape, and these produced a pronounced effect. The sounding-board, or more prop- erly, the reflecting board, was set up at one side of the platform, after the manner of the pulpits in Episcopal churches. (Fig. II.) The shape of the reflector was a quarter section of a pa- raboloid of revolution with the axis nearly horizontal . The frame was made of wood, and faced on the under side with hard plaster on wire lath. The finished reflector is shown in Fig. III. *W. C. Sabine, "Architectural Acoustics," Amer- ican Architect, 1900. t F. R. Watson, " Echoes in an Auditorium," Physical Review, Vol. 32, page 231, 1911. The results obtained were pronounced. Previous calculations showed that the sound would be di- rected in such a way as to confine the echoes to a small sec- tion of the audience. A canvas of the audi- tors showed this to be the case. Echoes were reported in the section expected, but the remainder of the audience had no such trouble. Some time later FIG. another reflector of the same shape and size was made and mounted over the center of the stage. This was done be- cause speakers regarded the raised pul- pit arrangement on the side of the stage as rather formidable . This second frame was much lighter in weight. It was constructed of small wooden rods in a most ingenious way by one of the University carpenters. (See Fig. V.) FIG. III. COMPLETED REFLECTOR. CONSTRUCTION OF REFLECTOR. It was faced with white oilcloth (see Fig. VI) instead of plaster, since it had been found that the oil cloth was a good reflector of sound and was much lighter in weight. The result obtained by its use confirmed the expectations as in the previous experiment. Reflectors of this kind have certain objectionable features. Thus, if the mouth of the speaker is at the focus of a paraboloid, the re- flected sound goes out in a parallel bundle and only a small por- tion of the audience gets the reenforced sound. This was found to be so in the two cases cited. Ex- periments showed the sound to be confined to the region calcu- lated. Auditors in this region reported an increased sound, while others outside this zone had no such reenforcement. To remedy this short- FIG. V. FRAMEWORK FOR REFLECTOR coming" and direct the sound to all the auditors would require a reflector of dif- ferent form. The results obtained indi- cate that this could be done by making- up a modified parabolic reflector to suit the conditions of the particular case. One other defect is the annoyance to the speaker. Thus; if his head is near the focus (Figf. VII), he is in a position to get concentrated sound from the audi- ence, i.e., coughing-, sneezing:, rustling of papers, etc. With the reflectors used, no such annoyance oc- curred. The two gentlemen who spoke the Right Rever- end Bishop Osborne, who used the reflector at the side of the stage, and Reverend Hugh Black, who used the reflector in the center of the stage each expressed his satisfaction with the reflector and reported no annoyance in speaking. The steep slope of the reflector eliminated any feel- ing of being ' ' shut in. ' ' A speaker standing- at the focus is not conscious of the presence of the reflector unless he turns around and looks at it. The advantages possessed by such a suitably desigfned re- flector are perhaps two in number . First, it serves to cut off the sound which passes to walls that may produce acous- tical disturbances, and second, to direct this sound usefully to auditors at a dis- tance from the speaker. Both of these effects were obtained in the auditorium at the University of Illinois. It is not planned to use the reflector at the latter place, since, as already indicated, the echoes can be eliminated by the instal- lation of false walls in the dome. It FIG. VI. REFLECTOR OVER PULPIT. seems likely that such a reflector would be useful in a hall where the walls could not conveniently be modified. It would be especially adapted for use in churches or halls where the position of the speaker is confined to a small space. * * See Architectural Review, Vol. I, Plate LVIII, December, 1912. FIG. VII, [Reprinted from the PHYSICAL REVIEW, N.S., Vol. II., No. i, July, 1913.] ON THE BEADED CHARACTER OF THE CATHODE RAY LINE AS REVEALED BY INSTANTANEOUS PHOTOGRAPHS TAKEN AT SHORT RANGE. BY CHAS. T. KNIPP. THE magnetic spectrum, so called, of cathode rays has been investi- gated by Birkeland, Strutt, and Thomson, 1 and is generally con- ceded to be due to the want of uniformity necessarily associated with the use of an induction coil. It was early shown that similar effects may be obtained by using an electrostatic instead of a magnetic field. Recently, while photographing at short range the carriers, atomic in size, of both positive and negative electricity that accompany the cathode beam, I was impressed with the beaded character of the cathode ray line. The distinctness and regularity of the beads suggested that their origin might possibly be other than a want of uniformity that accompanies the induction coil or static machine discharge, or other than the presence of secondary rays. APPARATUS AND MANIPULATION. The apparatus employed was that described in a recent number of the PHYSICAL REVIEW. 2 The modifications necessary were slight. The Wehnelt cathode was removed and in its stead an ordinary aluminum cathode was suitably mounted. The beam of cathode rays emergent from the canal passed between the nearly coterminous magnetic poles and electrostatic field plates and fell upon the photographic plate beyond. This range was about 2 centimeters. Seed's lantern slide plates were used. Mounting and exposing a plate to the action of the rays was briefly as follows: The circular plate, fastened to the movable brass disc 3 at three points by means of half and half wax, was placed in the cylindrical plateholder, which in turn slipped into position in the appa- ratus. After connecting the winch for turning the plate the glass containing vessel was sealed and the pump started. When the desired degree of exhaustion was reached, either with or without the aid of charcoal and liquid air, the electrostatic field was turned on and the discharge started. To get instantaneous photographs it was only neces- sary to rotate the plate while the discharge was passing. 1 J. J. Thomson, Conduction of Electricity through Gases, 2d ed., p. 633. 2 C. T. Knipp, PHYS. REV., XXXIV., March, 1912. 3 See Fig. i of article referred to above. 4 CHAS. T. KNIPP. Thus under varying conditions of deflecting fields (either magnetic, electrostatic, or both), aperture, vacuum and source of discharge, to- gether with varying conditions of resistance, self-induction, and capacity in the circuit, photographs of great diversity were possible. The short range that the carriers traveled enabled impressions to be received and recorded on the plate that at greater distances would doubtless be lost because of absorption. GENERAL CONSIDERATIONS. The electrostatic displacement of the cathode ray particle as recorded by the photographic plate is given by the equation Ae X - Irf (I) while the magnetic displacement is Be y = , (2) mv where A and B are constants depending upon the strength of the two fields respectively and upon the geometrical data of the discharge vessel. From these it follows that for a given range of velocities the greatest dispersion is to be had when an electrostatic field is employed. If there are present carriers having a wide range of velocities, falling off gradually from a maximum, then the time exposures when either field is employed should appear on the plate as a straight line shading off gradually in intensity as you recede from the geometrical or undeflected spot. The character of the instantaneous photographs will depend upon whether the discharge is intermittent or not. In the former case, the case of an induction coil discharge, the instantaneous exposures will be similar in shape and shading to the time exposures, only much less intense. If, however, the discharge is continuous, such as may be had from a high potential storage battery, the instantaneous exposures should reveal a continuous uniformly drawn out band similar in shading to the time exposure only much less intense. Uniformity in the direction of rotation of the continuous band may be expected only when the plate is rotated with uniform velocity. It would seem, then, that under the conditions just stated this arrange- ment of apparatus should reveal radiations that might have their origin in the discharge and possess energy enough to affect a photographic plate, as for instance (i) the presence of carriers due to ionization or secondary effects, (2) the possible emission of group velocity electrons from the surface of the cathode, or (3) group velocity electrons that may have their rise in the oscillatory character of the electric discharge. '] CHARACTER OF CATHODE RAY LINE. 41 In the first case, that of ionization, it is reasonable to expect that the photographs should show configurations that are fixed for both the time and the instantaneous exposures, but that would not necessarily be the same for a succeeding plate, and in general would not follow a definite law or sequence. In other words, the instantaneous photographs of the cathode ray line, produced by say an induction coil discharge, might show beads due to ionization and secondary effects, but it is not likely that the spacing of these beads along the line would follow any definite sequence though the spacings from instantaneous photograph to instantaneous photograph for a given plate more than likely would be the same. In the second case if the cathode gave off group velocity electrons the effect on the plate should be marked both for time and instantaneous exposures. Again, it does not seem clear that any definite spacing of the beads should be expected though the spacing, whatever it might have, would be characteristic of the metal. That the cathode gives off simultaneously group velocity electrons is by no means assured, though a careful study of the photographs lends that view some support. Finally in the case of group velocity electrons that have their rise, when the discharge is intermittent, to the oscillatory character of the discharge we can foretell quite accurately what the effect on the photo- graphic plate should be for both time and instantaneous exposures. Take the case of the discharge passing between the knobs of a static machine when the leyden jars that accompany the machine are included. The discharge obviously is oscillatory though damped rapidly. Let its general character be represented by Fig. I , in which the ordinates repre- Fig. 1. sent successive values of the quantity of electricity discharged and the abscissas the periodic time T. This period is given by the relation _ 2 / |~r^ ~ 2lr /\IC 4L*' which, as R diminishes, approaches the value T = 2w^LC. In words, the curve approaches a simple sine wave with no damping. 42 CHAS. T. KNIPP. If such an electrical pendulum could maintain itself in the case of our discharge vessel, the kinetic energy would remain constant and there would in consequence result but one group of group velocity electrons. This group would have the same velocity as the electrons in the case of a continuous discharge corresponding to the same discharge potential difference. If however R has a considerable value, as is the case that obtains in the ordinary operation of a discharge tube by a static machine or induction coil, the oscillations are damped as shown in Fig. i. The successive quantities discharged through the tube fall off rapidly, and hence the energy also falls off rapidly. This results, since both e and m remain constant, in a number of groups of electrons (one group corre- sponding to each crest) having successively smaller and smaller velocities. Take for example the case when the successive ordinates, both positive and negative, are proportional to 3.0, 1.5, i.o, 0.5, 0.32, 0.2, 0.12 centi- meters. If, as was suggested, the velocities of the resulting electrons in the cathode beam are proportional to these ordinates we should get by equation i, for the electrostatic displacement, distances proportional to O.I I, i.o, 10, 25, 70. And similarly by equation 2, for the magnetic displacement, distances proportional to 0.33, i.o, 3.3, 8.3. These dis- placements drawn to the same scale are set down in Fig. 2. Hence the Fig. 2. number of beads appearing on a given photographic plate, other condi- tions remaining constant, is, roughly, inversely as the damping of the oscillatory discharge which gives rise to them. The degree of exhaustion would also have an important bearing on the appearance of the beads. For a given set of conditions, such as in the example above, we should expect that the higher the vacuum the greater the velocity of the group electrons and hence the less the displacement. However, if the vacuum is too high the oscillations after the first one may not be able to get through the discharge vessel, and for very high vacua we should expect but the one group. On the other hand if the vacuum is low the velocity of the successive groups will be low and hence the larger the displacements. The latter may be so large for group electrons corre- sponding to oscillations after the first that these groups may be driven off the plate by the deflecting field. For low vacua the absorption will be considerable and this may be sufficient to prevent the slower moving groups from reaching the plate, or, if they do reach it, as may be the case CHARACTER OF CATHODE RAY LINE. 43 Hid 51 32.58. l .22 6 . e U O en js i ' G C O O O O a "a 6 6 . % & S 'o o S, rt c c c .2 .2 .2 000 CJ QJ &) c c c 888 T3 *T3 T3 cu \ I Fig. 10. Fig. 12. Fig. 13. Fig. 15. Fig. 14. Fig. 16. PLATE II. CHAS. T. KNIPP. VOL. II.- No. i. J CHARACTER OF CATHODE RAY LINE. 45 taneous exposures show a second and several a third dot in the direction towards the center of the plate. It is interesting in this connection to note that the first time exposure also shows the retrograde rays, i. e., carriers atomic in size and charged positively and hence deflected, in this photograph, away from the center. The conditions for Fig. 5 were nearly the same as in Fig. 4, except in the second half of the revolution a capacity of two leyden jars was included as shown in 6, Fig. 6. The connections for the first half are shown in a of the same figure. The undeflected spots are first shown, then the plate was turned through an arc during which the deflecting field X was on, after which X was reversed for a time and then again reduced to zero. The leyden jars were now included, as shown in Fig. 6, b, and Fig. 6. the sequence of exposures repeated. Unfortunately the reproduction does not show all of the finer markings of the negative. A number of the exposures on the negative show as many as four beads. In the succeeding photographs the tube was replaced by the objective containing the diaphragms. The three photographs, Figs. 7, 8, 9, con- stitute a series of instantaneous exposures in which all the conditions were kept constant except the vacuum. In these an 8 inch Leeds coil was substituted for the 6 inch Kohl coil. The connections were those of a, Fig. 6. The method of exposing each plate was to give the plate a quarter turn, then stop for a few seconds before proceeding on round. The first photograph, Fig. 7, shows the beads in a striking manner. In the second, Fig. 8, the vacuum was some higher and hence the displace- ment of the first group is less. The exposures on this plate show peculiar markings in the neighborhood of the undeflected point which may be due to ionization or secondary effects. These markings together with others that appear at the side of each instantaneous photograph are distinctly shown in the third photograph of this series, Fig. 9. The effect of an increasing vacuum is to cut off the subsequent groups. Traces of retrograde rays are visible in nearly all of the time exposures on these three plates. 46 CHAS. T. KNIPP. [15SS In the next three photographs, Figs. 10, 12, and 13, the induction coil was replaced by a Wehrsen static machine. Smaller values of X were also used. In Fig. 10 the connections were made as sketched in Fig. n. As is readily seen the discharge takes place at B without preparation whenever a spark passes at A. The volume of the discharge was con- siderable. Most every instantaneous exposure on the negative shows li il fl Fig. 11. beads. In the photograph reproduced in Fig. 12 the inductances and leyden jars were removed and connections were made direct. The vacuum was quite high. The peculiar markings shown in Figs. 8 and 9 again appear. These markings also appear very distinctly in the first half of Fig. 13. It would thus seem that they are not dependent upon the source of the discharge. To get still further evidence on the possible cause of the beads that so persistently appear on the cathode ray line I followed a suggestion made by Mr. O. H. Smith, graduate student in physics, and who assisted me in making a number of the exposures. If these beads are due to the oscillatory discharge then possibly additional evidence may be had by photographing simultaneously the negative crest. This could be done by mounting two exactly similar canals with their attending equal electrostatic fields diametrically opposite in the apparatus, so that either in turn may serve as the cathode. The plate with this arrangement to be turned but a half revolution. The negative crests (corresponding to the troughs in Fig. i) should appear on the plate as instantaneous photo- graphs diametrically opposite to the corresponding photograph for the positive crests. Indeed, this point may be tested with the apparatus as originally constructed by giving the photographic plate a half turn then interchange the connections after which the turn is completed. A plate thus exposed should show negative crests, obviously not simultaneously with the positive crests, but negative crests due to oscillations accom- panying a series of later discharges, and, so far as comparing the position of the negative crest with the positive trough is concerned, should answer equally well. VOL. II. No 5",. ' ] CHARACTER OF CATHODE RAY LINE. 47 The second half of Fig. 13 was taken under the above conditions. It shows that cathode rays do proceed from the anode. Their presence and position may be accounted for by the negative crests of the damped oscillatory discharge. In this photograph they did not, however, accom- pany each discharge, but only about every fourth one, though careful measurements show that the groups that are recorded correspond in general to the troughs in the first half. In Fig. 14 the static machine was replaced by the 8 inch Leeds induction coil, the vacuum was rather low, and X was made 1, 800 volts (see Table I.). On this plate the negative crests appeared in great numbers due in part to the plate being turned more slowly in the second half. For the most part their positions correspond to a trough in the first half, as may be seen by the arc drawn on the photograph. It seems strange, however, that this photograph shows no negative crests corresponding to the fiist trough. In the next, Fig. 15, X was made 3,000, otherwise the conditions were the same as in the preceding photograph. In this negative crests appear in the second half corresponding to two troughs in the first half. In the last photograph exposed, Fig. 16, the tube was again inserted. The vacuum though not recorded was high. In turning the plate it was halted twice, possibly for one or two seconds, in each' half turn. Again the points appearing in the second half correspond to carriers having a lower velocity than in the first half. In comparison with Figs. 4 and 5 it is evident that the vacuum was too high, since apparently only the first positive and first negative group electrons were formed. CONCLUSION. It appears from the photographs reproduced in this paper that in most cases the beaded effect of the cathode ray line may be accounted for by the oscillatory character of the electric discharge. However a number of the photographs show beads whose spacing along the cathode line is not in agreement with that that should follow for damped oscillations. These may be due to ionization or secondary effects, or possibly due to group velocity electrons given off by the cathode. The position of the cathode seems to have but little or no effect upon the general character of the beads. The strongest, and in some respects the most convincing evidence pointing to the oscillatory discharge as the origin of the beads is furnished by the photographs showing the negative crests. These crests in most every instance correspond to the troughs in the beaded line as shown in Figs. 13, 14, 15, and 16. 48 CHAS. T. KNIPP. [1S?E S D Admitting that the evidence submitted is sufficient to show that an oscillatory electric discharge under proper conditions (conditions which were met in a number of the foregoing photographs) results in a beaded cathode ray line, it seems that we have here a possible explanation of the beading of J. J.Thomson's molecular lines. 1 This conclusion, it seems to me, follows naturally because of the intimate relation that exists be- tween the cathode rays and the positive rays which form the molecular line. LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS, March, 1913. 1 Philosophical Magazine, August, 1912, p. 237. ON THE PRESENT THEORY OF MAGNETISM AND THE PERIODIC SYSTEM OF CHEMICAL ELEMENTS JACOB KUNZ ABSTRACT The Eighth International Congress of Applied Chemistry,. V. XXII, p. 187. The paper discusses the following topics : 1. Fundamental assumptions. 2. Experimental facts, diamagnetism, additive and non-additive proper- ties. 3. The periodic system of the elements and their magnetic properties. 4. Thermomagnetism. 5. The magneton of Weiss and the degrees of freedom. It is shown that the elementary charge of electricity can be deter- mined by the magnetic properties, the average of six values being e= 1.53. io- 20 . Reprinted from the ASTROPHYSICAL JOURNAL, Vol. XXXVIII, No. 2, Sept., 1913 THE USE OF THE PHOTO-ELECTRIC CELL IN STELLAR PHOTOMETRY PRELIMINARY NOTE BY W. F. SCHULZ The great sensitiveness of the photo-electric cell has been shown experimentally by Elster and Geitel, 1 by Nichols and Merritt, 2 and by J. G. Kemp. 3 From the results of these investigations it seemed that such a cell might be used to measure the light from fixed stars, and its variation. The following is an account of some successful preliminary experiments in an attempt to make such measurements. Diagram of apparatus Several cells of the form shown in the accompanying diagram were prepared in the following way. The anode was a platinum wire about o . 5 mm in diameter, bent into a rectangular loop about iX ij cm on the side, the terminal passing through a glass sleeve 3 or 4 cm long. On the wall of the tube facing the plane of this loop was a layer of potassium which formed the cathode. In order to have good contact at the cathode a layer of silver was deposited on and around the platinum terminal on the inside of the bulb. The 1 Physikalische Zeitschrift, 13, 468, 1912. 2 Physical Review, 34, 476, 1912. 187 Ibid. (2), i, 274, 1913. i88 W. F. SCHULZ bulb proper was about 5 cm in diameter. Potassium was distilled from a similar bulb into a second one, then poured into a pocket in the tube just outside of the bulb of the photo-electric cell and finally distilled upon the silver surface surrounding the cathode terminal. A little hydrogen gas was then introduced by heating a strip of palladium contained in a side tube. A potential-difference of 560 volts D.C. was applied to the electrodes P t and P 2 , P z being negative, with a lamp resistance of 3000 ohms in series with the cell. When the circuit was closed for a few seconds the bright metallic colors of the hydrogen compound appeared at once on the potassium. There was a uniform soft glow over the entire surface of the metal, the rest of the bulb being non-luminous. It was found necessary to use a rather high potential-difference with a resistance. When a potential- difference of 300 volts with little or no resistance was applied, the discharge took the form of an arc rather than that of a glow, and the current rose rapidly, in one case even melting the electrode. The circuit was broken when the surface of the potassium had assumed a brilliant violet-blue color and the hydrogen was carefully pumped out and was replaced by a small quantity of helium. All traces of oxygen were removed from the helium by passing it through a tube in which potassium was evaporated, before intro- ducing it into the cell. The photo-electric cell was next connected in series with a sensitive galvanometer and the lamp resistance, and a potential-difference of 300 volts was applied. The light from a small gas flame was allowed to fall on the metal of the cell, and the pressure in the latter was varied by small steps until the galva- nometer deflection was a maximum. The- tube was then sealed off and proved to be constant for a period of several months. For measuring very small intensities of light two different methods were used. In the colder winter months, especially in the open observatory, the temperature of the cell was so low that the natural leak through the dark cell was negligible, and the photo- electric current was measured directly by the rate of deflection of a quadrant electrometer. Toward the spring, however, when the temperature rose, the natural leak through the cell increased rapidly PHOTO-ELECTRIC CELL IN STELLAR PHOTOMETRY 189 with the temperature, and it was found necessary to compensate this current by means of an independent circuit as shown in the diagram. The anode of the cell was connected to a storage battery of 1 60 cells, the negative terminal of which was earthed. The cathode was earthed through a high resistance R t and connected through a discharge key to one pair of quadrants of a Dolezalek electrometer. In the compensating circuit a battery of 3 cells sent current through a variable resistance R 2 R 3 of 20,000 ohms, and the negative terminal was earthed. The other pair of quadrants was connected to R 2 R 3 by means of a traveling plug. By this arrange- ment the "dark current'' could be completely neutralized. V r was varied from 150 to 320 volts. This was not quite the upper limit at which the cell could be used, but 350 volts was too large, and the photo-electric current reached a value beyond that of saturation. R! was a very high resistance of xylol with just a trace of pure alcohol. The sensitiveness of the electrometer was such that a potential difference of 20 volts on the needle and i . 4 volts between the quadrants produced a deflection of 120 mm at a scale-distance of 2 meters. The deflections were very steady. The cell was tested by the light from a small incandescent lamp, which was cut down by passing it through two large crossed Nicol prisms. The cell was mounted in a light-tight box, carefully blackened inside, and closed by means of a shutter. A long closed tube was screwed into the opening of the box, and the lamp placed in this at 1.5 meter distance from the cell. The Nicols were inserted between lamp and cell, with a device for measuring and varying the angle between them. The candle-power of the lamp measured on a two-meter photometer with Lummer-Brodhun screen was approximately 0.003 a t 6 volts. The deflections of the electrometer were easily read even when the planes of polarization made an angle of 85 with each other. The intensity of the light which passed through an opening of i sq. cm area at the cell was therefore o. 003 X cos 2 &5/ 1 5 2 =0.000010 candle meters. It has been shown by Angstrom that the energy flowing from an amyl acetate lamp is approximately 10 8 gram calories per square cm at a distance of i meter. Assuming the Hefner unit and the 190 W. F. SCHULZ candle-power to be equal and the distribution of energy to be the same in both lamps, we find that the quantity of energy incident on the cell is approximately 0.000010X10 8 gram calories or 4. igX 10 6 ergs. This produces a deflection of the electrometer which is easily read. So far the light from two stars has been measured by means of this cell; in December 1912, that of Capella and in April 1913, that of Arcturus. The cell in its light-tight box was mounted on the i2-inch equatorial at the observatory of the University of Illinois, and placed in such a position beyond the focal plane of the objective that the circle of illumination on the sensitive surface of the cell had an area of about i sq. cm. On the cold December nights the natural leak through the cell was almost zero, and the photo-electric current was measured by the rate of the electrometer deflection. With 40 volts on the needle and 1 60 volts on the cell, the rate of deflection at a scale-distance of 2 meters was 20 mm in 30 seconds. With 200 volts on the cell, the rate was 18 mm in 20 seconds. These deflections were repeated without difficulty. In April 1913, another set of readings was taken with the light from Arcturus. This time the dark current had to be compensated. With 60 volts on the needle and 250 on the cell, the deflection due to the photo-electric current alone was 22 mm. This was reduced to zero each time by varying the resistance R 3 . With 60 volts on the needle and 300 on the cell, the deflection when the cell was exposed to the light of Arcturus was 48 mm; with 60 volts on the needle and 325 on the cell the deflection was 190 mm; and with 80 volts on the needle and 325 on the cell the deflection was 248 mm. The sensi- tiveness of both cell and electrometer can be increased. These measurements seem to show that it is possible to use the photo-electric cell for astrophysical investigations. The present research is being continued along various lines. It is planned to compare the sensitiveness of the photo-electric cell with that of the selenium cell, and to study the influence of temperature upon the "dark current," the effect of the wave-length of the incident light upon the lower limit of sensitiveness, and the use of various alkali metals for the sensitive layer. PHOTO-ELECTRIC CELL IN STELLAR PHOTOMETRY 191 These measurements were made at the suggestion of my friend Dr. Jakob Kunz, to whom I am deeply indebted for the benefit of his invaluable experience in making the cells and for assistance in conducting the experiments. UNIVERSITY OF ILLINOIS May 19, 1913 (Reprinted from the PHYSICAL REVIEW, N.S., Vol. II.. No. 3, September, 1913.] THERMAL AND ELECTRICAL CONDUCTIVITIES OF THE ALKALI METALS. O BY J. W. HORNBECK. I. INTRODUCTION. NE of the first successes of the modern electron theory consisted in its very simple explanation of the constant ratio of the thermal and electrical conductivities for the metallic elements. However, a closer study of the conduction of heat and electricity through metals, of their thermo-electric and magnetic properties, showed that the simple theory, which considered the electrons to move freely through the metal, was unable to explain the manifold and complicated phenomena in a satisfactory way. It was first assumed, in the theories of Riecke, Drude, J. J. Thomson and H. A. Lorentz, that the electrons are free and share the heat motion of the atoms; but this assumption leads to a number of contradictions. When one determines TV, the number of free electrons per cubic centi- meter, by the method of the conductivities for heat and electricity for the different metals, values are found which differ greatly 1 from those derived from the Peltier effect. Moreover, the experiments of Rubens and Hagen show that the electrical conductivity of metals for alternating currents of very high frequency remains practically the same as for steady forces, and the values of N which follow from these data are impossible 1 in view of the known values of the specific heat. Furthermore, Lees 2 measured the thermal and electrical conductivities of a number of metals down to the temperature of liquid air and found an increasing deviation from the law x _ 4 c? ;~5? ^ A change in structure has a large effect on the thermal and electrical conductivities. For instance it has been found recently 3 that the re- sistance of mercury at 4.2 absolute drops suddenly from o.n to zero. Small impurities have large effects. Metals and alloys often behave in opposite ways. For example, the heat conductivity of the metals de- 1 J. J. Thomson, Corpuscular Theory of Matter, pp. 76, 84. 2 C. H. Lees, Phil. Tran., Royal Soc., Vol. 208, p. 381, 1908. 8 H. Kamerlingh Onnes, Com. Phys. Lab. of Univ. of Leiden, No. 124, p. 23. 218 J. W. HORN BECK. creases slightly with increasing temperature, while for the alloys it in- increases with the temperature. Moreover, the ratio \/ where 7 is some constant, and from this equation we know v as a function of T. The constant term hn/2 has no effect in the present application of the Planck theory. If / is the mean free path and t the time during which the electron moves from one atom to the other, then t v = -. The force acting on the electron in the field E' is E'e, and the acceleration E'e a = . m The mean time during which this force acts is t/2 seconds and hence the field superposes a velocity at E'el u - . 2, 2mv The number of electrons passing through unit cross-section per unit time is NE'el Nu = , 2mv and the current density . A7 i = Nue Whence Nlve 2 _ Nlve*. \ Ei : hn ' For the quantity of heat energy passing through unit area per unit time, we have 22O J. W. HORNBECK. i SEj. i -..dEidT dT H = - Nvl -T = - Nvl -j= -3- = X -j . 3 d# 3 dr d# d# And Hence X 4 , . (3) Substituting in (3) the values of EI and dEi/dT, we have hn X 4 7 2 /& 3 3 I e kT oT ~ z e z k T If hn/kT is small, we can expand the exponential functions and equa- tion (4) for the higher temperatures assumes the form X _4 2 ) ~vT ~ 3 T " As T increases, according to equation (5), the values of \/ c r at o r e. Fig. 11. of taking observations and to indicate the degree of consistency obtained at different temperatures. In the tables which follow these "specimen runs," merely the final results are recorded. VOL. II.] No. 3. J CONDUCTIVITIES OF ALKALI METALS. 233 Meaning of Symbols. In all the data tables the following notation is used: r lt rz = balance-resistance on potentiometer dial for thermo-couples No. i and No. 3. r z = balance-resistance for thermo-couple No. 2 at middle of tube (or rod). r' = balance-resistance when reading P.D. ~7e fn p c t-a.'tvTr e Fig. 12. i, w 2 , u 3 = temperatures corresponding to resistances r lt r z , r s . UQ = temperature of the brass jacket. t m = %(u' + ^2) = temperature for which the values of than the diameter of the circle. The horizontal b_< "'' cross wire of the telescope was then sighted at b a to obtain the electrostatic deflection for 1/2 turn, the difference in the cathetometer readings between Fig 2 . b and a giving the amount of this deflection. The diameter of the circle was measured by placing the leg of a square against the plate glass window, and moving the square along till the edge of the circle at one half turn was in line with the other leg of the square. The same was done for the other side of the circle at the cathode. The difference between the two positions gave the diameter to within I per cent., as close a measurement as could be warranted by the slight fuzziness of the boundary of the beam. It was found that the lime would continually deteriorate and fall off from the hot Pt so that the beam would weaken and fade away with continual use. This necessitated the raising of the temperature of the Pt to bring the beam back again to distinctness. Thus during the course of 312 J. B. NATHANSON. [SECOND [SERIES. an experiment, the temperature of the Pt was intermittently raised from red to white heat. DISCUSSION. The values of e/m vary from 1.27 to 2.07 X io 7 , giving an average value of 1.61 X io 7 . This agrees favorably with Wehnelt's value of 1.48 and Knipp's value of 1.5, but is less than Classen's value of 1.773 obtained by a photographic method. The values of v vary from i.oo to 1.75 X io 9 cm. per second, giving an average value of 1.39 X io 9 . We would of course expect v to vary with the different temperatures employed. It might be instructive to check this value of v by another method. If V is the potential difference between anode and cathode, then we have from the equivalence of electrical and kinetic energy, V = ^ 2 V. \ m Supplying in this equation V = 1,000 volts, and e/m = 1.61 X io 7 , v is found to be 1.79 X io 9 cm. per second. This is somewhat higher, but of the same order, than the value of v experimentally obtained. However the actual difference of potential between anode and cathode had it been carefully examined, by means of a sounder, would have been found less than 1,000 volts. TABLE I. Distance between the electrostatic plates = 6.60 cm. Amperes, Gausses, H. Volts, V. Cm., z. Cm., 3 zr. elm X io-7. v X io- 9 . 1 3.30 18.84 81.3 1.01 10.1 1.71 1.62 2 3.99 22.78 81.2 0.85 7.7 1.39 .21 3 3.33 19.01 79.5 1.08 10.0 .56 .14 4 4.70 26.84 119.5 0.98 6.4 .27 .09 5 3.20 18.27 80.0 1.10 10.0 .64 .49 6 3.75 21.41 119.3 1.33 7.7 .46 .20 7 3.43 19.58 79.5 0.99 9.3 .59 .44 8 2.90 16.56 120.0 1.94 10.2 .70 .43 9 3.62 20.67 83.0 1.01 8.1 1.44 .20 10 2.90 16.56 120.0 1.72 10.3 1.91 .63 11 3.61 20.61 126.0 1.30 8.7 1.71 .53 12 3.35 19.13 43.0 0.43 8.9 2.07 1.75 13 4.20 23.98 120.0 1.05 7.2 1.49 1.29 Mean . 1.61 1.39 Returning to the values of e/m given in Table I., we notice that they vary somewhat among themselves. It seems that Wehnelt 1 had the same experience, for his table shows e/m to vary from 1.34 to 1.8 1 X io 7 . 1 Ann. d. Phys , 14, p. 425, 1904. ] DETERMINATION OF e/m AND v. 313 Since the method of this investigation is so different from Wehnelt's method, there seems to be no other conclusion than that the cause of the variation of e/m lies in the nature of the Wehnelt cathode itself. It was previously mentioned that the lime was continually disappearing from the hot Pt necessitating now and then the raising of the temperature of the Pt to obtain a sharper beam. Other recent work in this laboratory on the Wehnelt cathode shows quite conclusively that the activity of the hot lime, when supplied by Bank of England sealing wax, falls off rapidly with use the current rising to successively lower and lower maxima each succeeding day when heated to the same temperature. It is evident, due to the sputtering of the hot lime cathode together with the probable complex character of the lime obtained from the sealing wax, that the source of the negative carriers of electricity is not a constant one. Slight variations in the heating current made correspondingly very large variations in the density of the cathode beam. This inconstancy must account in a large measure for the variation of e/m. The disturbing effect of introducing the cathode between the electro- static field plates was less than the error due to the variations just men- tioned. This was shown to be the case by introducing the hot Pt strip carrying the lime up through a slot in the lower plate and adjusting so that the cathode beam, when bent into a circle by the strong magnetic field, just grazed the upper surface of this plate, the electrostatic field being zero. In addition it might be said that, apart from all quantitative measure- ments, the helical method is most beautiful in its nature, and the appa- ratus serves very excellently as a demonstration piece for the magnetic and electrostatic deflection of cathode rays. In conclusion I take this opportunity of expressing my thanks to Pro- fessor A. P. Carman for the facilities that were so kindly placed at my disposal, and to Dr. C. T. Knipp who made this work possible by his kind help and suggestions. LABORATORY OF PHYSICS, UNIVERSITY OF ILLINOIS, June, 1913. [Reprinted from the AMERICAN JOURNAL OF SCIENCE, Vol. xxxvi, Decem- ber, 1913.] ART. LI. On the Use of Sealing Wax as a Source of Lime for the Wehnelt Cathode ; by NELLIE !N. HORNOR. IN the Wehnelt* cathode as first employed various metallic oxides were used as salts. Those of calcium, barium, and strontium gave an abnormally large discharge of negative elec- tricity. The sign of the electrification depends upon the metal used and also upon the class of the salt.f Willows and Picton;): used nickel and platinum strips for the cathode, while Richard- son employed both the tube and strip methods, and recently Sheard || used the tube method. The conditions affecting the efficiency of this form of cathode have also been studied by Horton,!" Garrett,** and Wilson.ff In the work by Willows and Picton, referred to above, they found that when using a pressure of -002 mm Hg and up, a volt- age of 36, and a temperature of 1100 degrees Centigrade, there was a decided increase in the activity of the salt when the cathode had stood cold over a period of several days or weeks. They also found a greatly increased stream of electrons on making the discharge after it had been broken for a time, the heating current continued the while. The accumulation of electrons in the heated lime was dependent upon the interval of time. It has been known for some time that ordinary sealing wax makes a fairly good source' of lime. The Bank of England wax seems quite satisfactory. Its use, however, was until recently confined to the Cavendish laboratory. For some time it has been evident that its behavior as a lime is different than that of the oxides which are generally used. Hence the fol- lowing investigation, in which the object is a study of the activity of this source of lime together with the various con- ditions best suited for its efficient working. Description of Apparatus. A sketch of the apparatus used is shown in fig. 1. M.N is a two liter spherical flask, S' is a drying bulb, B' the heating circuit, C the cathode, and A the anode. The aluminium disc G' was connected through a reversing switch K 1 to the galvano- *Phil. Mag., vol. x, July, 1905. t J. J. Thomson, Proc. Camb. Phil. Soc., vol. xiv, 1906. tPhys. Soc., London, Proc., June, 1911. Phil. Mag., vol. xx, 1910. || Phil. Mag., vol. xxv, March, 1913. If Phil. Trans. Sec. A, vol. ccvii, 1907. ** Phil. Mag., vol. xx. October, 1910. ft Phil. Mag., vol. xxi, May, 1911. 592 Hornor Use of Sealing Wax as a Source of meter and to earth. A high potential cabinet T furnished the voltage, the positive terminal was connected through a water resistance to earth and to the anode and the negative through FIG. 1. 40 60 Time in 120 160 2-40 280 a switch K to the cathode. A voltmeter, YM. and an induc- tion coil, #, were connected to the switch K as shown. 1, 2, 3, 4, an d are re d wax joints. The method of mounting the cathode was that recently described by Knipp.* A K alder D'Arsonval galvanometer, 67, of a fair degree of sensitiveness was employed. *Phys. Rev., vol. xxxiv, March, 1912. Lime for the Wehnelt Cathode. 593 Method. The electrons fell upon the disc 6r', located opposite and about 4 mm from the cathode, and the resulting current was indicated by the galvanometer. With each galvanometer reading, which was the mean of two deflections, the pressure, FIG. 3. 30 60 90 120 Time in minutes 180 210 240 270 discharge voltage, and heating current readings were taken. The heating current was kept strictly constant. The pressure was also kept practically constant by occasional pumping. After mounting the platinum strip, a very small piece of the red wax was placed centrally upon it. The wires D and E* were then connected to the heating circuit and the current was 594: Hornor Use of Sealing Wax as a Source of FIG. 4. 3.0 2.7 T 2-l X 1 ' 8 0-l.S tt. 1.2 S .9 20 40 T\ me \n \nour3 60 80 FIG. 5. w 1.2 1.0 B ij- x .6 G. i* * c ^ 3 O \ \ \ \ \ \ A ? \ ^ \ ^ =N>. ~0 0- o-o t 0- 20 40 60 80 100 120 140 Time in mmute5 .Lime for the Wehnelt Cathode. 595 gradually increased until the disc of lime became white. The lime was thus deposited on the platinum strip. The tube was then placed in position, sealed, and the apparatus evacuated until the pressure was -OlS" 1111 of mercury or less. Pressures ranging from '003 to -Q4: mm were used. The apparatus was usually allowed to stand over night after evacuating to allow the P 2 O 6 to absorb the moisture. The heating current was adjusted until the temperature of the platinum was that corresponding to a light cherry -red. FIG. 6. r 4 ^ 2 ^~~ ^-o =3 =3 =0 ^H ff -^>- BOK= =CF= ^^ =Sr- s' "" / ^ ? 40 80 120 160 200 MO fl JO J20 360 400. Discharge in \Jolts Since it was necessary to renew the lime frequently, a reliable thermo-junction connection was nearly impossible and hence no attempt was made to determine the temperature. It was, however, kept strictly constant during any given run or set of runs. The discharge circuit was closed, the time noted, and the galvanometer watched for the current to start. When a cathode with fresh lime was heated the first time the discharge did not start immediately but only after from ten to thirty minutes if conditions were favorable. An induction coil may be used to start the discharge, but this complicates matters as there seems to be a gradual rise due to the ionization caused by the induction coil discharge. The cathode stream may also be started more quickly by making the heating current larger for a short time; however if this is done the increase to a maximum and the maximum itself are not shown, only the part of the curve due to the decay is obtained. Discussion of Curves. The effect of changes in the heating current is shown by curve 1, fig. 2. A very small change in this current, in fact one which the eye could scarcely detect on the ammeter where two scale divisions read 1/10 of an ampere, produced quite an appreciable effect upon the galvanometer deflections. 596 Hornor Use of Sealing Wax as a Source of After two hours the heating current became fairly steady and a smooth curve, from A to B, was obtained. The cathode was allowed to stand cold with the vacuum up for two days. On heating to the same temperature and starting the discharge again the current rose to a maximum value in an hour and then remained comparatively steady for the rest of the run. The steady current value shown in curve 2, fig. 2, was very little smaller than the maximum, which in turn was much smaller than the steady value for the preceding run. After five days another run was made with the same platinum strip and lime heated to the same temperature. This run gave a maximum less than the steady value for the second run, as shown by curve 3. It has the same general characteristics as curve 2. The discharge voltage for these curves was approximately 400 volts, the heating current 4'63 amperes, and the pressure varied from -005 to -016 mrn Hg. In the last two curves the heating current was steady. The curves in fig. 2 indicate that the activity of the red wax decays with time. This is also shown in a striking manner by curves 1, 2, and 3, fig. 3. The maxi- mum value of the current during any given run, after the lime had been cold from 1 to 4 days, was always less than the steady value of the current for the preceding run. Apparently when the lime is allowed to become cold it is not able to regain the activity it had at the end of the previous run. However, the activity that it does acquire it regains quickly. The relation between the maxima and the number of hours between them is shown by fig. 4. Evidently these maxima decrease very rapidly at first. When the lime is used for the first time it is very difficult .to adjust the heating current to a value that will give smooth curves similar to 2 and 3 in fig. 2. The form of the curve is more likely to be that shown in curve 1, fig. 3. In this the number of electrons emitted for the first two and one-half hours in- creased very slowly, when suddenly it rose to a very high max- imum and then almost as suddenly fell to a much lower steady value. The temperature was that corresponding to cherry-red. This sudden and very high maximum indicates that most of the electrons which may possibly be emitted under these con- ditions acquired sufficient energy to escape almost simultane- ously and thus caused, as it were, an explosion. Curves 2 and 3, in fig. 3, again show the same characteristics as curves 2 and 3 in fig. 2. After the lime has once been heated, the sub- sequent currents start much more easily and rise to a maximum more quickly, suggesting that the electrons are in a state more favorable to emission. The beam was visible to the eye in curves 1, 2, and 3, fig. 3, from A, B, and 6 y on. If the discharge voltage was cut off while the heating con- Lime for the Wehnelt Cathode. 597 tinned, the current obtained on again closing the discharge circuit was in every case smaller than it was just before breaK- ing. This is shown by fig. 5. The behavior of the lime seemed to be much the same as though it had been allowed to stand in the cold, except that the effect was not so pronounced. This shows that the decrease in activity for short intervals of no dis- charge was slight, yet definite, if the lime was kept hot. This result does not agree with that of Willows and Picton, who observed, for the salts that they used, a decided increase in activity under the same conditions. Data on the saturation voltage were obtained as follows : for a given heating current and a discharge voltage of 40 volts the run was continued until the current became steady, after which the voltage was advanced by steps of 40 volts at inter- vals of 10 minutes, the maximum current being recorded each time. The curve in fig. 6 shows the results obtained. There was saturation at 200 volts. The Bank of England wax upon analysis was found to have the following principal constituents : calcium sulphate (gyp- sum), barium sulphate (heavy spar), mercuric sulphide (cinna- bar), and shellac. Summary. It was shown that when Bank of England sealing wax is used as the source of lime there is a falling off in the activity with time. When a maximum is reached most of the electrons are emitted during the first run. When the discharge is broken while the heating current is maintained there is a slight falling off in the negative stream. The above results are exactly opposite to those obtained by Willows and Picton using calcium oxide on a platinum strip, while they agree in part with the observations of Sheard, who found that the activity for cadmium iodide and iodine, with the tube method, decreased during any given run. The saturation voltage was found to be 200 volts. There was a falling off in the maxima for successive runs, and the steady current for any given run was usually much smaller than that for the preceding run with the same lime. In conclusion, the writer takes pleasure in thanking Profes- sor A. P. Carman for the facilities of the department, and Dr. C. T. Knipp for suggesting the problem and assistance in car- rying out the details of this investigation. Physical Laboratory, University of Illinois. Acoustical Effect of Fireproofed Cotton-Flannel Sound Absorbers Reprinted from Engineering News January 29, 1914 BY P. R. WATSON! Cotton-flannel was found to be a fairly good absorber of sound, during a recent investigation of the acoustic properties of the Auditorium at the University of Illi- nois. It is easy to obtain and to install; it is also com- paratively cheap; but, unfortunately, it is inflammable The question then arose as to the effect of fireproofing upon the sound-absorbing qualities of cotton-flannel. A search through the literature on the subject did not yield very much, and apparently little has been done on this particular phase of the problem. In 1902, Norton 1 published an account of some experimental tests of the sound-absorbing qualities of materials that were already fireproof. Sabine 2 describes some experiments in which hair felt was covered by burlap attached by silicate of soda. In neither of these investigations was it apparent just what effect the process of fireproofing had. The author then took up the problem of testing flannel before and after fireproofing. The observations were taken by Sabine's method. 3 In a room, about 20x20 ft., cleared of all furniture, an organ pipe was sounded for several seconds and then stopped. The time taken for the sound to die out was noted by an observer who made the record electrically on a chrono- graph drum. This observation was repeated at least ten times. A similar set of measurements was then, taken when a large sheet of outing flannel was hung in front of one of the walls. A third set was taken with a sheet of fireproof ed cotton-flannel in place of the unfireproofed. A summary of results follows; each record is the aver- age of at least ten measurements. Cotton-flannel EmDtv Date June 26 June 30 Average 3.26 2.25* 2.30 ''-The permanent fireproofing of fabrics was briefly de- scribed in a news note in "Engineering News," of Oct. 10, 1912. Ed. fAssistant Professor of Physics, University of Illinois, TJr- bana. 111. Empty room Un- fireproofed Fire- proofed sec. sec. sec. 3.3 2.3 2.4 2.4 2.3 3.2 2.2 2.3 3.3 2.1 2.2 The results indicate that the fireproofing, for the con- ditions of the experiment, did not materially change the sound-absorbing properties of the cotton-flannel. This result was rather surprising since it was expected that the fireproofed material would be the poorer absorber of sound. The two samples used were cut from the same piece of goods. The unfireproofed piece was fluffy and rather thick, while the other piece in process of fire- proofing was soaked in a solution, then squeezed flat by being run through a wringer, and finally dried. 1 1 seemed likely that the fireproofed piece would absorb sound less readily, since it was now squeezed into a closer texture and its interstices apparently more or less filled with the fireproofing substance. The experiments, how- ever, showed it to have the same effect as the unfire- proofed. Each sample was hung about four inches from a plastered wall, and pleated in folds so that each width of the flannel (30 in.) covered only a foot. The total area of each piece when in place for the experiment was about 9x12 sq.ft. The flannel cost about 15c. per yard including fireproofing. PREPRINTED FROM THE ASTROPHYSICAL JOURNAL AN INTERNATIONAL REVIEW OF SPECTROSCOPY AND ASTRONOMICAL PHYSICS VOLUME XXXIX MAY 1914 NUMBER 4 A DETERMINATION OF THE SUN'S TEMPERATURE BY GLENN A. SHOOK INTRODUCTION In 1906 Moissan carried out a number of experiments upon the vaporization of metals. 1 He placed the temperature of his furnace at 3500 C. and made the statement that all known elements vola- tilize at that temperature. Now it is thought by Schulz that the temperature of the furnace must have been considerably above 3500 C. and probably as high as the sun's photosphere which he sets at 5400 C. 2 He argued that owing to the large current used by Moissan there was an enormous amount of energy which had no adequate escape by conduction or radiation and which therefore must have raised the temperature of the furnace up to the point where it was checked by the melting and evaporization of the lime- stone of which it was constructed. He moreover asserts that the volatilization of the metals is not to be regarded as complete. We also find the following remarks in regard to molybdenum and tungsten: Molybdenum. The 1 50 grams were not fused by a current of 500 amperes and no volts. After applying 700 amperes and no volts for seven minutes, 1 Annales de chemie et de physique, 8, 151, 1906. 3 Astrophysical Journal, 29, 33, 1909. 277 278 GLENN A. SHOOK the metal was fused but nothing evaporated. After twenty minutes 56 grams were distilled. Tungsten. After applying 500 amperes and no volts for 5 minutes the metal was not yet fused. After applying 800 amperes and no volts for twenty minutes, boiling commenced but only 25 grams distilled. It thus appears that the volatilization is partly a question of time, and when we remember that the sun's photosphere is probably at a temperature of 8000 C. or 9000 C. and that such a temperature has existed for years and not minutes, we must conclude that all elements in the sun are necessarily in the gaseous state. The following hypothesis which has been advanced by a num- ber of investigators 1 is confirmed by the present research. In the first place the material of the sun is " gaseous," that is, it follows the extended law for gases. Secondly, the radiation that reaches us comes from the reversing layer alone or at least only from the superficial layers of the photo- sphere. Thirdly, there is a relatively large drop in the temperature at the reversing layer. If there is considerable scattering of light due to the gases of the reversing layer, then the light that reaches us comes only from a small depth. Moreover, the scattering is greater for blue light than for red, consequently the blue part of the spectrum must be relatively weaker than the red part. Hence, if the temperature falls off rapidly as we move outward radially through the reversing layer we should expect the temperature for blue light to be less than that determined for red light. Also as we move across the sun's disk, we should expect the apparent temperature to fall off rapidly as we approach the limb and we should, moreover, expect the temperature gradient for blue to be greater than that for red. This is precisely what the writer finds. The sharp boundary of the photosphere is additional proof of the gaseous scattering. That the scattering prevents us from seeing beyond a shallow depth of the reversing layer may be shown by a rough calculation. 1 Secchi, Le soleil, i, Book III, chap, iv, p. 267; 2, Book VII, chap i, p. 299; Schwarzschild, "Ueber das Gleichgewicht der Sonnenatmosphare," Gottingen Nachr., Math. Phys. Kl., 1906, pp. 1-13; Abbot, The Sun, p. 236. THE SUN'S TEMPERATURE 279 The law of molecular absorption is expressed by the following formula : or log^ -- kh * where 7 = the intensity of light incident upon the absorbing medium; 7=the intensity of the transmitted light; & = the fraction of light absorbed by unit thickness of the medium; and h = the thickness or height of the absorbing layer. Using Abbot's 1 values for the transmission of the atmosphere above Mount Wilson we have: Wave-length in/u. ........... 0.4 0.5 0.6 0.7 Percentage of transmission. ... 76 89 95 97 Taking the Mount Wilson atmosphere, which is about 10 miles, as our unit thickness, the length of a column of gas for an extinction of 99 per cent or a transmission of i per cent for a wave-length of o . 4 JLC becomes log o . 01 - = 0.24/2 0.4343 or h = iS. S , that is, the column would have to be 185 miles if the gas had the same density as the Mount Wilson atmosphere. The relative densities of the photosphere and the Mount Wilson atmosphere may be determined by means of Boyle's Law as follows: Let the pressure, volume, and absolute temperature of the former be p', v', and T', and the corresponding quantities for the latter be p, v, and T. We may now write: pv=RT and hence pv _T pV~T f 1 Nature, 81, 97, 1909. 280 GLENN A. SHOOK Assuming that the pressure of the reversing layer is about 5 atmos- pheres, that its mean temperature is 7000 A., and that the temperature of the earth's atmosphere is 250 A., we obtain the relation : _ 250 5X?/ 7000* Writing d s for the density of the reversing layer and d e for the density of the earth's atmosphere, the above equation becomes: ^250X5 d e 7000 Hence a column of gas on the sun sufficient to produce an extinction of 99 per cent at wave-length o . 4 JJL would have to be i8.5XioX-^ r-=iooo miles high. In this manner Table I was constructed TABLE I Wave-Length Miles 0.4 /A ................................... IOOO 0.5 .................................... 2400 0.6 .................................... 5200 0.7 .................................... 8600 Since the radius of the sun is 435,000 miles, it is readily seen that the radiation which we are utilizing for the estimation of temperature comes from only the outermost solar layers. It is also observed that for short wave-lengths the depth to which we are able to penetrate is smaller than that which obtains for the longer wave-lengths. EXPERIMENTAL METHOD FOR THE DIRECT DETERMINATION OF THE SUN'S APPARENT TEMPERATURE The method employed by the writer for the determination of the sun's apparent temperature is an application of Planck's formula for the visible spectrum. In this method the brightness of the sun's disk is compared photometrically with the brightness of the filament of a miniature incandescent lamp for three different colors. To carry out these observations the Department of THE SUN'S TEMPERATURE 281 Astronomy of this university kindly permitted the use of their small observatory, which is equipped with a six-inch equatorial telescope. A new eyepiece was constructed, providing a receptacle for the lamp between the eye-lens and the field-lens. A new finder, provided with a micrometer scale and parallel hairs, was also attached to the telescope. An image of the sun is formed by the objective in the focal plane of the eyepiece. The .incandescent lamp is adjusted until its filament lies in the plane of the image of the sun's disk. If one looks through the telescope when it is directed toward the sun he sees the image of the lamp-filament superimposed upon the image of the sun's disk. Now by varying the current through the lamp the filament can be made to disappear against the bright background of the sun's image. When this condition obtains, the temperature of the filament is equal to the apparent black-body temperature of the image, and by means of Planck's formula the apparent black-body temperature of the sun's disk can be esti- mated if the temperature of the filament is known as a function of the current through the lamp. In the present investigation the lamps used were calibrated by the Bureau of Standards. The eyepiece that was used in the equatorial and which contained a lamp receptacle was fitted into a small telescope and this arrangement was used by the bureau in calibrating the lamps by means of their standard black body. They furnished for each lamp a table containing a series of temper- atures and the corresponding currents through the lamp. The error which might be caused by reflections from the lamp globe and eye- piece lenses was thus eliminated. As a matter of fact, the entire filament will never disappear since all parts are not of the same intensity, but one always uses the central portion of the tip and this is practically uniform in intensity. The filament (Fig. 2) may be moved about easily to any point on the disk, which is represented by the dotted line, by means of the right ascension and the declination screws. Fig. i shows the reticle of the finder with the scale and parallel spider lines. These parallel lines are adjusted so that their distance apart is equal to 282 GLENN A. SHOOK the diameter of the sun's image, and they are, moreover, always parallel to the ecliptic. The axis of the lamp is generally maintained perpendicular to the ecliptic. The lamp is connected in series to a few storage cells, an adjustable resistance, and a milliammeter (Fig. 3). FIG. i FIG. 2 This arrangement of lamp and eyepiece, which is the result of some experimenting, was found to be the most satisfactory. With an equatorial as small as this one the image is only about i cm in diameter, and in order to investigate the intensity along any radius, i.e., along a distance of 0.5 cm, with any accuracy it is necessary ii mm- FIG. 3 to have a rather large magnification. In order to obtain a clear image the field-lens is also indispensable. Again, with the present arrangement the globe of the lamp just about fills up the space between the two lenses and therefore it is not in focus; conse- quently when one looks at the tip of the filament the contour of the globe is scarcely noticed. If an eye-lens of longer focal length were used, the globe would cause a distortion of the image. THE SUN'S TEMPERATURE 283 The problem of diminishing the intensity of the sun's image to that of an incandescent lamp-filament presents no small difficulty. The intensity may be partly diminished by diaphragming down the objective, but on^e cannot resort solely to this method without seriously impairing the definition of the image. When the aperture is made as small as is permissible, an absorption glass may be used, but it is almost necessary to use three or more if the absorption coefficient of the arrangement is required in any calculation. The density of a single glass required to make the necessary reduc- tion in intensity is so great that it is impossible to measure its absorption coefficient with any accuracy. Since the absorption of these glasses is never absolutely general, i.e., non-selective, and since they differ slightly among themselves, it is necessary to measure the absorption factor of each glass for each wave- length used. Moreover, the optical properties of these glasses must be almost as good as those of the telescope objective; otherwise aberrations would result. It is for this reason that it is practically impossible to use a large telescope since the absorption glasses would have to be made with as much care as the objective of the telescope. In order to determine the best arrangement for the six-inch equatorial used in this investigation a number of observations were carried out upon the moon's disk. The most conspicuous craters were carefully studied with a full objective and then with a number of diaphragms having apertures of different size. In this manner it was found that an aperture of about i . 5 cm still produced good definition. In addition to this diminishing of the aperture three absorption glasses were also used. The objective of the finder was also stopped down and in addition an absorption glass was used. Monochromatic light was produced by placing colored glasses directly before the eye- lens R (Fig. 3). It is practically impossible to obtain a single colored glass which is even approximately mono- chromatic. Four colors of Jena glass were obtained from Petitdi- dier, Chicago namely, red, yellow, green, and blue. The red is remarkably good, transmitting only a red band, and that rather narrow. The yellow, which appeared monochromatic to the 284 GLENN A. SHOOK unaided eye, was found to transmit almost the entire spectrum. The green contains a faint band in the yellow but it is free from blue. The blue glass transmits a band in the red, as is usually the case with blue glasses, and also faint lines in the green. While, according to our information, these are the best glasses that can be obtained, it is readily seen that they were unsuitable without some modifications. A detailed study of monochromatism of various kinds of glass was then undertaken. A quantity of different kinds of colored glass was obtained and these glasses were all examined separately by means of a spectroscope, and then different combinations were tried until the best arrangement was obtained. The Jena glasses were found to be superior to any examined but a combination of three different glasses was found to give the best results. For example, some green glass transmits blue light but no red, while nearly all blue glass transmits some red; consequently a combination of the two is practically free from red without any perceptible reduction of the blue light. In this manner it was possible to obtain combinations for red, green, and blue light all of which are practically monochromatic. The search for monochromatic yellow was, however, futile. It seems almost impossible to obtain a glass or a combination of glasses which produces yellow and excludes all the other colors in even a moderate degree. The fact that a glass for a particular color may contain a faint band of another color is often of no consequence, providing that consistent readings may be made, and a very narrow band is not always necessary if the band contains only one color. For instance, we may have a rather wide red band, but so long as there is no orange included in the band a good photometric balance can always be made, and the wave-length used would always be the central part of the band. The difference between this wave-length and the true optical center of gravity is too insignificant to consider in this particular problem. There are other methods for producing monochromatic light, but none is very well suited to this particular problem. The spec- THE SUN'S TEMPERATURE 285 troscopic eyepiece designed by Mendenhall 1 for pyrometers using the disappearing-filament principle is best adapted to this particular apparatus, but it was rejected for several reasons. In Menden- hall's pyrometer a short horizontal section of the lamp-filament and the superimposed image are focused upon the slit of an auxil- iary direct-vision spectroscope. The slit of the spectroscope is vertical so that the field is crossed by three spectra, the middle one corresponding to the lamp-filament. A diaphragm is so placed in the focal plane of the eyepiece of the spectroscope that only the desired region of the spectrum is transmitted to the eye. In order that this central band may be wide enough to make a photometric comparison it is necessary to use a very thick lamp-filament, and this is impossible when a large magnification of the image is required as in the present investigation, for then all parts of the filament would not be in focus. Even with a fine filament there is some distortion of the image. Furthermore, any such spectroscopic method diminishes the intensity of the light considerably, making it necessary in the blue and violet region to open both slits of the instrument very wide in order to get sufficient light to make a balance. If this is done, we have no longer strictly monochromatic light, and we may as well employ colored glasses. With a colored glass one sees the filament and sun's image directly so that he always knows just what part of the disk he is on, but with the spectroscopic eyepiece this of course is not the case, and he must depend entirely upon the finder. It has been shown by a number of experimenters that the disappearing-filament principle is by far the most sensitive photo- metric scheme that we have, and it is particularly adapted to this problem, since one can move the filament about to any point on the sun's image, and make a temperature measurement at that point. The wave-lengths of the monochromatic glasses were deter- mined by means of a Lummer-Brodhun spectrophotometer" made by Schmidt and Hensch. The same instrument was also used to determine the absorption coefficients of the absorption glasses. 1 Physical Review, 33, i, 1911. 286 GLENN A. SHOOK DATA AND RESULTS i. Wave-lengths of the monochromatic glasses. The readings of the arbitrary scale of the Lummer-Brodhun spectrophotometer for the three colored glasses used are given in the following tables: TABLE II OCULAR SLIT = 0.05 CM SLIT No. i, 50 RED GLASS GREEN GLASS BLUE GLASS Blue End Red End Blue End Red End Blue End Red End 616 546 734 654 994 750 618 546 732 654 994 748 614 544 734 6 5 2 990 750 618 546 736 654 994 748 616 542 736 652 994 752 616 546 734 656 1,000 750 616 544 734 656 1,002 748 616 546 736 654 996 75 614 546 736 654 994 748 614 544 734 654 996 754 Mean q8o Mean 604. Mean 868 The blue light was very faint, hence the readings are not quite so consistent as in the case of the red and green. The wave-lengths in ju, corresponding to these arbitrary scale readings, are as follows: TABLE III Lummer-Brodhun Scale Reading Wave-Length in M Red glass S8o 0.661 Green glass 694 0.537 Blue glass 868 0.446 2. Absorption factors. In determining the absorption factor R for any particular glass the zero reading of the Lummer-Brodhun spectrophotometer was taken before and after the observations with the glass. The standard lamps were connected in parallel to the same mains and the voltage was controlled by a rheostat. THE SUN'S TEMPERATURE 287 Red Light TABLE IV L.-B. No. 580 Ocular Slit = 0.05 cm Zero Reading Volts Glass No. i Volts Slit No. I, C C/ C 1 Oi 02 ->i Oj Glass No. i. > .^ I = 5 Glass No. 2. . . ............... #2 = 11. Glass No. 3 .................. #3 = 11. whence (red) . The absorption factors for the green and blue glasses, obtained in the same manner, are 340 and 656 respectively. The lamps used for estimating the sun's temperature were cali- brated in a small telescope of 2.68 cm aperture. The distance from the filament to the aperture was 59.8 cm. In the observa- tory telescope the distance from filament to aperture was 157.5 cm and the aperture was i . 49 cm in diameter. The ratio of the two solid angles gives the reduction factor for the telescope. We therefore obtain: TT (2.68) a .7r (i.49) a = 4 "(59. 8)'* 4* (157. 5)' The resultant reduction factors for the three colors then become : Foro.66i/A # = 22.3X1725 = 38,500 (i) 0.537/x # = 22. 3X 340 = 7580 (2) 0.446/4, # = 22. 3X 656 = 14,610 (3) 3. Temperature measurement of the sun's disk. The distance across the sun's disk was measured by means of a micrometer scale in the finder of the telescope, but the number corresponding to the center of the disk would of course change if the lamp were raised or lowered. For the observations carried out for the red and green light 54 corresponded to the center of the disk and 69 to the extreme edge or limb. THE SUN'S TEMPERATURE 289 The radius of the disk is thus equal to 15 divisions on the scale of the finder. In the following tables the readings of the ammeter are given for various distances from the center of the disk. When the filament was adjusted to the desired point on the disk the current through the filament was varied continuously until the tip had the same intrinsic intensity as the region surrounding it or until it disappeared against the disk. The following (Table V) is a sample of the data obtained for the variation of the temperature with distance from the edge to the center of the disk. TABLE V AMMETER READINGS FOR GREEN LIGHT 69 68 67 6 4 80.0 84.0 86.0 91 .0 82.0 84.5 87.5 Qi-S 79-5 83.5 87.0 89.5 81.0 83.5 86.5 89.0 81.0 83-5 88.5 91 .0 81.0 83.0 87.5 9i-5 81.0 85-0 87-5 89-5 82.0 82.5 86.5 9-5 8i.5 82.5 87.5 9i-S 81.0 82.5 85.5 90.0 Mean. . . .81. i Mean 83 . 5 Mean 87.0 Mean 91.0 60 54 69 69 69 92.0 93-5 81.5 80.0 80.0 93-o 92.5 82.0 80.5 80.0 9 I -5 93-5 8i.5 8i.S 8i.S 9i-S 93-0 82.0 80.5 80.0 93-o 91 .0 8i-5 80.0 80.5 93-0 92.0 8i.S 80.0 82.0 92.5 92.0 81.0 82.0 80.0 9i-5 92.0 82.0 80.0 80.5 92.5 91-5 81.5 81.0 81.0 91.0 9i 5 81.5 8i-5 80.0 Mean. 92. 2 Mean. 92. 3 Mean of 30 observations 81 .0 In this case the observation on the edge, i.e., 69, was repeated and it is seen that the agreement is better than might be expected considering the uncertainties of such measurements. 2QO GLENN A. SHOOK Instead of reducing these readings to temperatures of the sun's disk, a curve was plotted for each color, co-ordinating ammeter readings and distances from center of disk. For any particular distance, the corresponding ammeter reading may be obtained directly from the curve. This gives a better average of all the values taken across the disk. 4. Reduction of an observation. Since it is somewhat easier to use Wien's formula for the reduction of these temperatures, that formula will be used for all the calculations. A temperature esti- mation will also be made by means of Planck's formula to show the difference in the two results. We shall consider in detail only the data obtained for red light, as the same method applies equally well to green and blue. Let T r equal the black-body temperature of the sun's disk, E' the intensity of radiation incident upon the objective of the tele- scope. Also let T be the apparent temperature of the sun's image and E the intensity of the energy transmitted by the absorbing media of the telescope. Wien's formula may now be written for the two cases as follows: log E' = hk^Y/ (4) and \ogE=k l -k 2 ^. (5) Subtracting (5) from (4) we obtain: E' _ But where R is the reduction factor of the telescope. Whence ^_j^_logff ^ \ogRX T T k 2 14,500X0.4343 From (i): 7^ = 38,500 and X = o.66i . THE SUN'S TEMPERATURE 291 Therefore whence L log 38,500X0.661 k = >J =0.00048: 14,500X0.4343 ^7 = ^-0.000482. (6) Now consider curve i, Fig. 4, for scale divisions, 54, i.e., the center of the sun's image; the ammeter reading is 67.2, and this corresponds to a temperature of 1317 C. or 1590 A. If we sub- stitute this value for T in equation (6) we obtain for T the 68 66 64 62 60 69 67 65 63 61 FIG. 4 59 57 55 53 temperature of the sun's disk, a value of 6803 A. In this manner data were obtained for curves 2, 3, and 4, Fig. 5. As we move from the center of the disk toward the limb, the temperature falls off more rapidly for the shorter wave-lengths, but near the limb it falls off less rapidly. There has always been considerable discussion as to the best value of the constant C 2 . The value used by Lummer, Prings- heim, Paschen, and Wanner is 14,500. Our own Bureau of Stand- ards 1 also accepts the same value but the value determined by 1 Bulletin Bureau of Standards, 3, No. 2. 2Q2 GLENN A. SHOOK Holborn and Valentiner is much lower 14, 200.' Again, Nernst and Wartenberg use the value i4,6oo. 2 To show the effect of the 7000*) 6000 5000 4000 3000 69 67 65 63 57 55 53 61 59 FIG. 5 variation of this constant on the value of the temperature of the sun, the following values were calculated for red and blue light: TABLE VI c, Red 0.66/A T Blue 0.446 M 14,000 6135 4310 14,100 6211 4348 14 2OO 6320 4386 14. 3OO 6404 4425 14,400 i A.