From Current Literature

Acoustics

Technique of microphone calibration. Exhaustive knowledge of all the properties of a microphone, which is one of the principal instruments in the technique of acoustical measurements, is unquestionably necessary for the exact quantitative treatment of results. In this respect, the detailed exposition of the theory and method of calibrating a condenser microphone given in the work of S. Ballantine is of great interest. In the first part of the work, the method is considered for measuring the e.m.f. developed by the microphone, referred to unit pressure on the microphone membrane, as a function of frequency; a method of electrostatic excitation is described, in which the pressure on the membrane is produced by electrostatic forces acting between the membrane and a lattice electrode placed in front of it; next, a method of calibration by means of a thermophone is presented (a detailed exposition of the theory of the thermophone is given), and, finally, a method of exciting the microphone by a piston membrane. In the second part, a method is described for measuring the microphone e.m.f. referred to unit pressure in a sound field not distorted by the presence of the microphone; the pressure is measured by means of a Rayleigh disk. In the concluding part of the article, data are given on the change in pressure on the microphone membrane due to diffraction of sound, on the influence of the resonance properties of the air cavity in front of the membrane, and on the directional characteristic of the microphone. In the appendices, theoretical considerations are given on separate questions touched upon in the main text. (S. Ballantine, Journ. Acoust. Soc. Amer., 3, 319—360, 1932.)

Apparent decrease in loudness. The work of D. Laird, E. Taylor, and G. Willey contains the results of observations of an apparent considerable decrease in loudness at a relatively small diminution of the actual level. A number of observers were asked to note the moment at which the apparent loudness fell to \(^{1}/_{4}\), \(^{1}/_{2}\), and \(^{3}/_{4}\) of its initial value. The actual decrease in level, expressed in decibels, in fact proved to be smaller; moreover, as the loudness of the original sound increased, the observer’s error increased, while at low loudnesses (from 30 dB and below) the error is practically absent. The experiments were carried out with pure tones and withablytyped

From Current Literature

by a buzzing tone of the audiometer. The data obtained by the authors are summarized in 9 tables and illustrated by curves. (D. Laird, E. Taylor, H. Wille, Jr. Journ. Acoust. Soc. Amer., 3, 393—401, 1932).

Determination of the loudness of noise. In H. Marvin’s work the question is considered of the possibility of determining the loudness of noise by the method of comparing it with the loudness of a pure tone. For objective reading Marvin uses an audiometer with a characteristic corresponding to the change in the sensitivity of the ear with pitch; moreover, for levels from 0 to 30 db (taking as the initial level that which corresponds to a sound pressure of 0.001 bar) one characteristic was selected, while for levels from 30 to 60 db another was used, passing higher in the region of low frequencies, and, at frequencies greater than 1000 cycles, lower than the first. As sources of noise an electric motor, a refrigerator, and a transformer were taken. Marvin’s preliminary experiments showed that the results obtained by the method of comparison with the loudness of a pure tone agree quite well with the data of objective measurement. (H. B. Marvin, Journ. Acoust. Soc. Amer., 3, 388—392, 1932.)

Vertical recording on a disk. H. Frederick’s article contains a report on work carried out in the laboratories of Bell Telephone Co along the line of improving the technique of gramophone recording. Theoretical considerations and experience show that vertical recording, first applied by Edison, gives incomparably better results than the commonly accepted lateral recording. Frederick’s experiments indicate that vertical recording makes it possible to extend the transmitted frequency band up to 10,000 cycles, with a simultaneous increase of the range of transmitted loudnesses to 50 db. These possibilities are opened up chiefly by the considerable reduction of parasitic noise, which in lateral recording makes it necessary to cut off frequencies above 5000 cycles and strongly limits the range of loudnesses. Of interest also is the method of copying from wax described in the article, characterized by the use of cathodic sputtering of metal instead of the commonly used method of applying graphite powder to the wax. (H. A. Frederick, Journ. Soc. Mot. Pict. Eng.), 18, 141—163, 1932.)

Distortions of microphones and loudspeakers. A very interesting summary of data concerning the linear and nonlinear distortions of various types of microphones and loudspeakers is given by C. A. Hartman (to a considerable extent on the basis of the results of his own measurements). After a brief characterization of various kinds of distortions the author gives a method for calculating the clear factor of carbon and condenser microphones; for comparison with experimental data the corresponding curves are given. The last part of the work is devoted to distortions,

connected with the directional characteristic of electrodynamic-type loudspeakers (conical and with a flat diaphragm) and microphones (carbon and ribbon); in addition, data are given on the directional characteristic of a microphone concentrator (an ellipsoid of revolution with an opening of 50 cm and an eccentricity of 80 cm). At the end of the paper a bibliography is given. (C. A. Hartmann, ZS. f. techn. Phys., 13, 9—17, 1932.)

Calculation of mechanical oscillatory systems by the method of electromechanical analogies. In A. Forstmann’s paper a systematic exposition is given of the foundations of the method of electromechanical analogies, which has recently become very widespread in the field of technical acoustics. The paper contains: the general principles of the method, methods for constructing equivalent electrical substitution circuits, and sample calculations of certain apparatuses (a conical electrodynamic loudspeaker, an electromagnetic adapter for reproduction from gramophone records, an electromagnetic loudspeaker). It is shown that, from the point of view of the absence of linear distortions, the equivalent electrical circuit in the case of an electromagnetic loudspeaker must have a high natural frequency and sufficient damping; the latter circumstance helps eliminate distortions associated with the phenomena of the system’s transient regime. (A. Forstmann, H. F. Techn. u. El. Ak., 39, 11—18, 1932.)

Determination of the amplitude and phase of electrodynamic loudspeakers. In the experimental study of electrodynamic loudspeakers, it is often necessary to know the frequency characteristic of the system and the curve of the phase difference between current and displacement in the low-frequency region, where the natural period of the oscillatory system usually lies. For this purpose V. Binder developed a simple method that makes it possible to measure directly the amplitude of the loudspeaker diaphragm. The loudspeaker is excited by an audio-frequency generator consisting of a rotating disk, through whose slots a periodically interrupted beam of light falls on a photocell; the amplified photocurrent is fed to the loudspeaker coil. With an appropriate choice of the shape of the openings in the disk, a current sufficiently close to sinusoidal can be obtained. A second beam of light, passing through the disk at a certain angular distance from the first, falls on the diaphragm of the loudspeaker; since both beams are interrupted with one and the same frequency, when the diaphragm is observed the light spot appears motionless. The displacement of the light spot from the equilibrium position, observed with the excitation switched off, is measured by means of an ocular micrometer. By changing the angular distance between the two beams (counting along the circumference of the disk), the light spot is again brought to the positi-

to the equilibrium position of the membrane, after which it is not difficult to calculate the required phase difference between the current and the displacement. The membrane amplitude is read by establishing such an angular displacement between the two beams at which the light spot is farthest from the equilibrium position. The method gives good results only in the region of low frequencies (up to 200 hertz), where the displacement amplitudes are large (of the order of tens of mμ/A). The paper gives curves obtained by means of the method described. (W. Binder, Phys. ZS., 33, 85–87, 1932.)

Transmission of a wide frequency band. Recently a considerable number of works have appeared which, to one degree or another, touch upon the question of the importance of extending the transmitted band toward high frequencies. Some observations of interest in this respect are given in the work of Wills. The author gives a description of an electroacoustic circuit (microphone—amplifier—reproducer) constructed with allowance for uniform transmission of the frequency band from 30 to 15,000 hertz. The receiver is a condenser microphone in a low-frequency circuit (membrane resonance near 10,000 hertz), with a characteristic raised in the region of low frequencies (40–200 hertz) by means of electrical compensation. For reproducing sound, a unit consisting of two loudspeakers was used: an electrodynamic cone type for transmitting the band up to 6000 hertz, and an electrostatic one (with a polarizing voltage of 1000 V) for transmitting the band from 6000 hertz and higher. The resulting frequency characteristic of the whole circuit gives deviations from the mean line not exceeding ±5 decibels in the required range. Observations on the quality of transmission confirm the correctness of the idea of the need to extend the transmitted band: when the static loudspeaker is switched in in addition to the dynamic one, speech transmission acquires vividness, and the individual features of timbre are clearly distinguished; the transmission of music (string and percussion instruments) is likewise considerably improved. It must be noted that in transmitting such a wide band the requirements with respect to eliminating extraneous noises are greatly increased: footsteps in the studio, the turning of pages, etc. It is characteristic that when the static loudspeaker, radiating high frequencies, is switched in, the absence of plasticity in sound transmission is noticed much more distinctly—the sound is perceived as being emitted from one point. In reproduction from a gramophone record, the expansion of the transmitted band gave no result, since ordinary gramophones do not reproduce high frequencies. (W. Willms, ENT, 9, 68–70, 1932.)

Phenomena of the establishment of steady state and their significance in acoustics. Theoretical acoustics in most cases confines itself to considering phenomena of the established steady state, turning only in certain special cases (for example, in the field of architectural acoustics) to an analysis of the phenomena of the rise and decay of acoustic—

processes. The work of H. Backhaus, carried out in its experimental part jointly with E. Weise, shows that the phenomena of the establishment of a regime deserve much more serious attention. Direct experiments show that nonperiodic acoustic processes (both in the case of prolonged sounding and in the case of switching a sound source on and off) are of very great importance for the characteristics of a sound image. Backhaus investigated a whole series of processes of sound establishment (speech and music), recording the course of the phenomenon oscillographically and analyzing the records obtained by the method of harmonic analysis. The experiments show that the phenomena of regime establishment have relatively little significance only for the recognition of vowels, since, owing to the strong damping in the resonant bands of the organs of speech, the time of regime establishment here does not exceed a few thousandths of a second. Thus, for the recognition of vowels the perception of timbre is quite sufficient. Acoustic processes connected with the sounding of linking consonants (in connected speech) may be considered as processes of establishment of the vowel sounds following them; in this case it turns out that the characteristic features determining the recognition of these consonants consist not so much in the processes of sounding of “isolated” consonants as in the duration of establishment of the regime of the following vowel sound. According to Backhaus’s measurements, the time of establishment of the regime of the following vowel varies for different consonants from 0.025 to 0.12 sec. In the sounding of musical instruments the phenomena of a non-established regime have still greater significance: experiments have shown that, when transmitting an already established tone (when the sound increased and died away the transmitting loudspeaker was switched off), even an experienced musical ear cannot confidently determine the instrument being sounded. The time of regime establishment varies for different instruments from 0.035 sec. (saxophone) to 0.12 sec. (violin). Also characteristic is the circumstance that, in the process of sounding of an already established tone, the amplitudes of partial tones undergo considerable fluctuations; this phenomenon often determines the specific coloration of the sound of a given instrument, and consequently nonperiodic processes play an important role from the point of view of the aesthetic effect of instrumental music. In the concluding part of his work Backhaus reports the results of a study of the phenomena of regime establishment in various models of modern loudspeakers; in Backhaus’s opinion, the “dullness” of timbre characteristic of the reproduction of music by loudspeakers is due to the presence of “parasitic” decaying oscillations of low frequency. (H. Backhaus, ZS. f. techn. Phys., 13, 31—46, 1932.)

Problems of the acoustics of rooms from the standpoint of undistorted sound transmission (in particular, in sound cinemas) are considered in a new survey by F. Trendelenburg. The contents of the survey:

1) the influence of phenomena of sound reflection on the quality of sound transmission, 2) sound absorption and the duration of reverberation from the point of view of the perception of sound. The paper reports data, to a considerable extent already cited in previous review articles by the same author. (F. Trendelenburg, ZS. f. techn. Phys., 13, 40—58, 1932.)

The speed of sound in tubes at sonic and ultrasonic frequencies was again measured by C. Vance in glass tubes with diameters from 0.1 to 3.0 cm. The sound source was a quartz oscillator; the speed of sound (at frequencies from 30 to 200 kilohertz) was determined by the Kundt-tube method. Vance’s results do not agree with the theoretically obtained Helmholtz–Kirchhoff formula:

\[ V = V_0 \left[ 1 - \frac{C}{2} R(2\pi N)^{\frac{1}{2}} \right]; \]

according to Vance, the formula

\[ V = V_0 \left[ 1 - \frac{C}{D^2} - \frac{K}{D}(N)^{\frac{1}{2}} \right] \]

gives good agreement with experiment both at sonic and at ultrasonic frequencies.

In the formulas: \(V_0 = 331.77\ \text{m/sec}\), \(C = 0.001512\), \(K = 0.174\), \(N\) is the frequency, \(D\) and \(R\) are the diameter and radius of the tube. (C. B. Vance, Phys. Rev., 39, 737—744, 1932.)

Measurement of noise intensity. One of the first tasks of the commission for combating noise, organized as early as 1930 under the Union of German Engineers, was the measurement of the intensity of urban noises, caused chiefly by urban transport. The results of the measurements are given in the work of T. Bakoss and S. Kagan. The paper gives, first of all, a description of the most important methods for measuring noise intensity: objective (rectification of amplified microphone currents while establishing correspondence between the frequency characteristic of the apparatus and the sensitivity curve of the ear) and subjective (Barkhausen’s method, obtaining an audiogram from the determination of the “masked” loudness of a reference tone). In measuring the noise level on large squares in Berlin, the authors used both objective and subjective methods, which made it possible to establish the degree of comparability of the data obtained by the different methods. The authors give graphs of the noise level over the course of a day and audiograms containing the maximum, mean, and minimum values of the intensity of the noises. A comparative characteristic of various sources of noise contains the following data (values in decibels):

The authors also present the results of measurements of the noise level in a financial institution (Postcheckamt Berlin), in a room where work is carried out on 230 calculating machines. The average noise level is very high: 73 decibels. In conclusion, the authors give the results of a comparative study of data obtained by different methods; in agreement with previous data, the method of determining masked loudness gives, in comparison with the objective method, figures 10–15 decibels lower. (G. Bakos und S. Kagan, VDI, 76, 145–150, 1932.)

ELECTRICITY

Dielectrics

The structure of solid salts at high temperatures. The article is limited only to salts containing oxygen. The author distinguishes four types of crystal lattices: 1) a purely ionic lattice (containing at the nodes metal ions \( \mathrm{Me}^{+} \) and ions of the element \( \mathrm{R}^{-} \), the latter being surrounded by oxygen atoms O); 2) a lattice in which complex ions of both the type \( \mathrm{MeO}_{4} \) and the type \( \mathrm{RO}_{4} \) are equally possible (in this case the distances \( \mathrm{Me}—\mathrm{O} \) and \( \mathrm{R}—\mathrm{O} \) are equal or differ only very slightly); 3) a lattice also containing complex ions of both types (\( \mathrm{MeO}_{4} \) and \( \mathrm{RO}_{4} \)), but differing from the preceding one by the nonidentical arrangement of the O atoms in the \( \mathrm{MeO}_{4} \) ions as compared with the \( \mathrm{RO}_{4} \) ions; and, finally, 4) lattices with neutral molecules. Several examples show how, under the influence of temperature, lattices of type (1) or (2) can transform into a lattice of type (3). The question of equilibrium among these three types of lattices is examined. The question of electrical conductivity is touched upon. (W. Iander, ZS. f. anorg. Chem., 192, No. 3, 236–244, 1930.)

On polarization in solids when current passes. In this work Böning develops ideas expressed by him earlier (see ZS. f. Fernmeldetechn., 8, 162, 1927; ZS, f. techn. Phys., 10, 82, 1929). The mechanism of polarization, according to Böning, is reduced to the absorption of ions in the surface layer of the dielectric. This point of view makes it possible to explain quite thoroughly a number of phenomena. It also sheds some light on the question of the breakdown of solid dielectrics and on the structure of detecting crystals. (ZS. f. Phys., 66, No. 9/10, 581–597, 1930.)

The crystal lattice from the standpoint of thermodynamics. Electrostatic calculations of crystal lattices, as is known, are associated with great mathematical difficulties. The author approaches the question from quite a different side. On the basis of thermodynamic considerations the lattice energy is calculated for the case of ordinary temperatures; then an approximate extrapolation to 0°K is carried out. (ZS. f. Phys., 67, No. 1/2, 127—134, 1931.)

Polarization of NaCl crystals under photoconductivity. As is known, prolonged passage of a photocurrent through a crystal (X-rayed NaCl) is accompanied by the formation of polarization, exactly as occurs in the case of an ordinary ionic current. The polarization is caused by the accumulation of volume charges at the electrodes; however, it cannot be said in advance whether these are ions or electrons. The work of Tartakovsky gives an answer to this question. With the aid of the Hall effect it was possible to show that, in the case of photoconductivity, it is precisely electrons that are the sources of the polarization. (ZS. f. Phys., 66, No. 11/12 830—833, 1930.)

Internal photoeffect in deformed NaCl. The primary photocurrent was investigated in crystals of X-rayed natural and annealed rock salt in the frequency interval from 410 μμ to 690 μμ. The influence of elastic deformation was manifested in a displacement of the maximum of the photocurrent toward long waves and in an overall weakening of the sensitivity to light. In some cases a gradual return of the maximum with time to its original value and to its original position was observed. (Podaschewsky, ZS. f. Phys. 65, No. 11/12, 799—805, 1930.)

Conductivity in solid electrolytes. The authors investigated transport numbers for a whole series of salts: BaF₂, BaCl₂, PbCl₂, PbJ₂, NaF, NaCl, KCl, and others. On the basis of these investigations one can judge which of the ions (positive or negative) carries the current. In this respect it proved useful to distinguish halide salts from alkali-halide salts. Whereas in the former mainly anions participate in conductivity, in the latter, on the contrary, conductivity is due predominantly to cations. For halides this holds at all temperatures up to the melting temperature; for alkali-halide salts, beginning at approximately 400—450° C, the mobility of the anions increases noticeably. At higher temperatures, ions of both signs participate in the conductivity of alkali-halide salts. It is precisely this that explains the fact that the formula characterizing the dependence of conductivity on temperature is often expressed as the sum of two exponential terms. (Tubandt, Reinold, Liebold, ZS. f. anorg. Chem., 197, No. 3, 225—253, 1931.)

Electrical conductivity and high-voltage polarization in crystals of Rochelle salt. Two interesting papers deal with the following questions: 1) The dependence of the polarization e.m.f. on the external potential difference and on temperature has been clarified. 2) It is shown that the exponential dependence of conductivity on temperature occurs not only for the “initial” (“true”) conductivity, but also for the “residual” conductivity (with changed parameters, of course). Decreasing as the temperature rises, the polarization disappears altogether at 190° C. This point is common to all the investigated field strengths. At temperatures above 190° C no formation of polarization was observed. 3) The role of impurities and their influence on the magnitude of the polarization has been clarified. (Gochberg and V. A. Ioffe, Zh. R. F. Kh. O., issue 62, 5, 1930.) 4) The question of the through (residual) current is examined. Comparing the amount of electricity stored at the electrodes under the action of direct current (charging current) with the amount of electricity calculated from the reverse-current curve (discharge current), the authors came to the conclusion that the so-called “through current” (i.e., that part of the current which does not go into the formation of volume charges) must depend on the polarization and, consequently, change with time. The “through” current increases as volume charges accumulate at the electrodes, reaching—by the time the stationary state is established—the value of the “residual” current. This result refutes the view that had prevailed until now of the “through” current as independent of polarization and constant in time. 5) Finally, the question of the influence on polarization of impurities diffusing into the crystal from the electrodes is once more investigated. (Gochberg and V. A. Ioffe, Zh. E. T. F., issue 5, 1931.)

On Ohm’s law in crystals of rock salt. In this question the results obtained by different authors, as is known, disagree with one another. Whereas Gochberg and Ant. Walter (ZS. f. Phys., 64, 392, 1930) obtained for the conductivity a constant value, not changing appreciably with increasing external potential difference, Kvitner and Beran (ZS. f. Phys., 64, 760, 1930), on the contrary, obtained a rather sharp dependence of the conductivity on the potential difference. Such a discrepancy, as Gochberg believes (ZS. f. Phys., 70, 635, 1931), contains nothing fundamental, and is due merely to the fact that the specimens studied in the two cases had different origins. The deviation from Ohm’s law observed by Kvitner and Beran should thus be attributed to chemical inhomogeneities in the crystals with which they were dealing.

Mechanism of breakdown of solid dielectrics. Two papers by Hippel are devoted to the theory of breakdown of solid dielectrics. The basic idea is that the author regards breakdown as purely

FROM CURRENT LITERATURE

an electronic phenomenon, contrary to the established tendency to ascribe an ionic nature to breakdown. The first article—which, incidentally, also contains some new experimental material—is devoted to the substantiation and development of this point of view (ZS. f. Phys., 67, 707–724, 1931.) Let us note that the very same idea of the electronic origin of breakdown was also expressed by Soviet authors (e.g. Sinelnikov, Zh. E. T. F., issue 1, 1932.) These conceptions may briefly be summarized as follows: an elementary calculation shows that the breakdown gradients prove sufficient to tear an electron from a lattice ion; in the crystal an electron avalanche is formed, quite similar to what—according to modern ideas—takes place in breakdown in gases.

The second paper by Hippel, which to some extent is a continuation of the first, is devoted chiefly to the question of the direction of breakdown in a crystal. The trajectories of the electrons (channels) can be observed with the naked eye, since the regions of the crystal along the channels turn out to be colored violet-blue. Such coloration at high potentials is in general observed for the first time. The direction of the channels makes it possible to judge the laws that govern the motion of the electrons, and reveals the atomistic meaning of the concept of “breakdown voltage.” At the end of the paper Hippel touches upon the question of the relation between the electrical and mechanical strength of a crystal (ZS. f. Phys., 68, 309–324, 1931.)

The question of the direction of breakdown is also the subject of a paper by Lass. The direction of the channels is conditioned by the crystallographic structure of the crystal. Lass dealt with an inhomogeneous field (the electrodes were a plate and a point). At high temperatures (about 600°C) the dependence of the direction of breakdown on the crystallographic direction appeared less distinctly: the crystal was pierced in the direction of the maximum gradient. (ZS. f. Phys., 69, 313–331, 1931.)

Conductivity of liquid dielectrics at high potentials. Studying the dependence of current on voltage in the case of a liquid dielectric, the author distinguishes three regions. At first (low potentials) the current increases in proportion to the applied voltage (this is the region of Ohm’s law); then the current becomes and remains approximately constant—something like “saturation” sets in (the “saturation” region); and, finally, in the third region (high potentials) a new increase of the current begins, but this time linear rather than exponential. The present work concerns conductivity mainly in this third region. The author studied the dependence of the current on the distance between the electrodes (the case of plane electrodes) at a constant field strength. Here an exponential dependence was found. This fact and a whole series of further considerations lead the author to the idea of the likelihood of ionization processes in a liquid dielectric at high

potentials. Ionization, naturally, depends on the nature of the liquid and on its homogeneity. The minimum voltage at which avalanche formation is possible is of the order of 30 kV/cm. (Nikuradse, Naturwissensch. 19, 233–234, 1931.)

STRUCTURE OF MATTER

A new determination of $\dfrac{e}{m}$ from the Zeeman effect. In a critical evaluation of the modern values of the fundamental physical constants, Birge drew attention to the fact that the values of the specific charge found spectroscopically and from the deflection of cathode rays differ noticeably from one another. The spectroscopic value of $\dfrac{e}{m}$ is equal to $1.761 \cdot 10^7$ m, whereas measurements with cathode rays, although they give fluctuating results, nevertheless converge to the value $1.769 \cdot 10^7$ CGSM. At the same time, in most summaries the value obtained by Backlin and equal to $1.761 \cdot 10^7$ is ignored. Since theoretical investigations could not indicate any reasons for such a discrepancy, it seemed expedient to subject to careful verification the results obtained up to now by both the one method and the other. A spectroscopic determination of $\dfrac{e}{m}$ was recently carried out by Campbell and Houston at the California Institute of Technology by determining the Zeeman splitting of the Cd line 6439 and the Zn line 6362. The magnetic field used was equal to 7300 gauss, and the Zeeman effect was photographed with the aid of a Fabry–Perot interferometer. As a result of careful determinations, the following was obtained

\[ \frac{e}{m}=1.7579 \pm 0.0025 \cdot 10^7 \; CGSM \]

—a value in good agreement with the former optical determinations, although also somewhat smaller than them. (J. S. Campbell and W. V. Houston, Phys. Rev., 39, 601, 1932.)

Determination of the specific charge of the electron by means of direct measurements on cathode rays. To clarify the reason for the discrepancy, indicated in the preceding note, between the values of $\dfrac{e}{m}$, it is also necessary to repeat with greater accuracy the direct measurements on cathode rays.

Kirchner proposed the following method for this purpose. If $v$ is the velocity of the electron and $p$ the accelerating potential difference, then

from the energy equation \(\frac{mv^2}{2}=eP\) it follows: \(\frac{e}{m}=\frac{v^2}{2P}\). A very precise determination of \(v\) is possible by the method earlier proposed by Kirchner (Phys. Z., 30, 773, 1929), with the aid of rapid electrical oscillations. Combining this direct determination of \(v\) with the precision measurement of \(P\), one can, from the preceding, find \(\frac{e}{m}\). Such measurements, after all corrections, led Kirchner to the following result:

\[ \frac{e}{m}=1.7585 \pm 0.0012 \cdot 10^7 \, CGSM. \]

This quantity, within the limits of error, agrees with the spectroscopic value of \(\frac{e}{m}\), whence it follows that the discrepancy mentioned, discovered by Børdjem, is explained by excessive confidence in earlier measurements of cathode rays. (F. Kirchner, Ann. d. Phys., 12/5, 503, 1932.)

Wilson photographs of particles associated with cosmic rays, made by Locher, showed that groups of penetrating particles are observed relatively often; the direction of the paths of these particles indicates that they come from a single source. Locher considers the following explanation the most probable. Penetrating particles arise when photons of cosmic rays act on atomic nuclei. The appearance of groups of particles indicates that two or more electrons are ejected simultaneously from one nucleus. Thus we are dealing here with “ionization of the nucleus,” or, what is the same thing, with artificially induced radioactivity under the action of photons of cosmic rays. (G. L. Locher, Phys. Rev., 39, 883, 1932.)

The fine structure of the visible absorption bands of bromine was subjected to a new investigation by Brown under Mulliken’s direction. Photographs of the absorption spectrum were made in the third order of a Rowland 21-foot grating (0.8 Å/mm). The absorption spectrum of bromine, like that of iodine and chlorine, should have a simple structure and consist only of two branches \(P\) and \(R\). A complicating circumstance is the isotopic structure of bromine. The two isotopes of Br contained in it in equal proportion, \(\mathrm{Br}^{79}\) and \(\mathrm{Br}^{81}\), should give three types of molecules: \(\mathrm{Br}^{79}\mathrm{Br}^{79}\), \(\mathrm{Br}^{81}\mathrm{Br}^{81}\), and \(\mathrm{Br}^{79}\mathrm{Br}^{81}\), whose quantities should be in the ratios \(1:1:2\). The characteristic feature of the bands belonging to the first two types of molecules consists in the presence of alternating intensity of the fine-structure lines—a phenomenon characteristic of molecules composed of two identical atoms. Such bands were indeed identified in a number of cases; however, owing to insufficient resolution, the ratio of intensities could not be determined. The numerical values of the constants of the molecule \(\mathrm{Br}^{79}\mathrm{Br}^{81}\), found by analysis

of the rotational structure of the bands of this molecule are as follows \([r_e\) is the radius, \(I_e\) is the moment of inertia, \(B_e=\dfrac{h}{8\pi^2 c\mu r_e^2}\), \(\alpha\) is the coefficient in the formula

\[ B_v = B_e - \alpha\left(v+\frac{1}{2}\right), \]

a single prime \( '\) indicates that the quantities refer to the excited state, a double prime \( ''\) to the normal state]:

\[ \begin{aligned} B_e'' &= 0.08091, &\qquad B_e' &= 0.0696,\\ \alpha_e'' &= 0.00028, & \alpha_e' &= 0.00062,\\ I_e'' &= 324.1 \cdot 10^{-40}, & I_e' &= 465 \cdot 10^{-40},\\ r_e'' &= 2.28 \cdot 10^{-8}, & r_e' &= 2.65 \cdot 10^{-8}. \end{aligned} \]