Showing papers in "Physical Review in 1922"

On a New Method for the Generation of Sound-Waves

Abstract: Pressure variation along a high-velocity air jet, produced by a pressure of 0.9 to 5 atm. above normal, was determined with a simple Pitot tube, and the periodic intervals of instability were located (Figs. 2 and 5).New Source of Sound; Resonator Actuated by a High-Velocity Air Jet.---It was found that the intervals of instability referred to above can be used for the generation of sound. (1) Bulb form. When the small orifice to a bulb is placed in one of these intervals so that the particles of air move in and out of the opening, pulsations like those of a siren are produced, the tones not being pure. The fundamental frequency depends on the volume of the bulb, the size of the orifice and the position in the jet, and may readily be varied from 1/10 to 5,000 per second. (2) Cylindrical form. When a simple cylindrical resonator is placed with one end in an interval of instability, pure tones are produced except in certain positions when overtones may be present. The frequency is the fundamental of the resonator and may be made as high as 125,000 per second by using a very short tube, about 0.5 mm. in length and in bore. With a hydrogen jet, the frequencies are, of course, 3.8 times as high. The efficiency of such sources is remarkable, intensities that are painful being readily produced. Practical forms of these generators are illustrated (Figs. 3 and 4).

Acoustic Wave Filters

Abstract: Acoustic Wave Filters Composed of a Series of Like Sections.---(1) Theory. Taking the impedance of any part of an acoustic circuit to be equal to the complex ratio of the applied pressure difference to the rate of change of volume displacement, it is shown that, neglecting dissipative forces, it is possible to construct a filter having limiting frequency values of no attenuation determined by the formul\ae{} $\frac{{Z}_{1}}{{Z}_{2}}=0$ and $\frac{{Z}_{1}}{{Z}_{2}}=\ensuremath{-}4$, where ${Z}_{1}$ is the impedance of the transmitting conduit circuit and ${Z}_{2}$ of each branch of each section. The impedance of any section depends on the inertance $M$ of dimensions mass per unit area squared, and the capacitance $C$ which has the dimensions of stiffness per unit area squared. If $M$ and $C$ are in parallel, $Z=\frac{\mathrm{iM}\ensuremath{\omega}}{(1\ensuremath{-}MC{\ensuremath{\omega}}^{2})}$, whereas if they are in series, $Z=i(M\ensuremath{\omega}\ensuremath{-}\frac{1}{C\ensuremath{\omega}})$. For instance, in the case of a closed chamber or resonator, $M$ and $C$ are in series and are equal to $\frac{\ensuremath{\rho}}{C}$ and $\frac{V}{\ensuremath{\rho}{a}^{2}}$ respectively where $\ensuremath{\rho}$ is the density of the medium, $c$ is the conductivity of the mouth, $a$ the velocity of sound and $V$ the volume. Formul\ae{} are derived for various assumed cases. On account of the uncertainty as to whether a tube may be considered sa having the equivalent inertness and capacitance connected in parallel or in series, the application of these formul\ae{} to actual cases is somewhat empirical. (2) Construction and test of filters of three types. Low-frequency-pass filters were made, for example, by two concentric cylinders joined by walls equally spaced and perpendicular to the axis. Each chamber thus formed had a row of apertures in the inner cylinder which served as the transmission tube. In one case the volume of each chamber was 6.5 ${\mathrm{cm}.}^{3}$, the radius of the inner tube 1.2 cm. the length between apertures, 1.6 cm. A chamber and one such length of the inner tube is called a section. Four such sections were found to transmit 90 per cent. of the sound from zero to approximately 3,200 d.v. where the attenuation became very high, resuiting in zero transmission up to about 4,600 d.v. where transmission again appeared, Other similar filters of different dimensions attenuated through wider or narrower ranges. The lower limit of attenuation was found to correspond within 8 per cent. with the formula: $f=(\frac{1}{\ensuremath{\pi}}){({M}_{1}{C}_{2}+4{M}_{2}{C}_{2})}^{\ensuremath{-}\frac{1}{2}}$. The upper limit was not predicted theoretically. High-frequency pass filters were made with a straight tube for transmission and short side tubes, for example, 0.5 cm. long and 0.28 cm. in diameter, opening through a hole with conductivity 0.08 into a tube 10 cm. long and 1 cm. in diameter. Six sections of such a filter would transmit about 90 per cent. of sounds above 800 but would refuse transmission to sounds of lower frequency. As would be expected, the cut off is not sharp. Filters with other dimensions were found to have an upper limit of attenuation varying from 450 to 2,300 d.v., agreeing with the formula $f=(\frac{1}{2\ensuremath{\pi}}){(\frac{1}{4{M}_{2}{C}_{1}}+\frac{1}{{M}_{1}{C}_{2}})}^{\frac{1}{2}}$, within about 13 per cent., on the average. The single-band filters made were a combination of the other two types, having side tubes leading to chambers of considerable volume. For instance, three sections each 5 cm. long and 0.5 cm. in diameter, with side tubes of the same size and 2.2 cm. long leading to a volume of 28 ${\mathrm{cm}.}^{2}$, transmitted between 270 and 370 d.v. The frequencies of the edges of the band of small attenuation are determined by the following formulae, ${2\ensuremath{\pi}f={[{M}_{2}{C}_{2}(1+\frac{{{M}_{2}}^{\ensuremath{'}}}{{M}_{2}})]}^{\ensuremath{-}\frac{1}{2}} \mathrm{and}}{2\ensuremath{\pi}f={[{M}_{2}{C}_{2}{(1+\frac{4{M}_{2}}{{M}_{1}})}^{\ensuremath{-}1}(1+\frac{{{M}_{2}}^{\ensuremath{'}}}{{M}_{2}}+\frac{4{{M}_{2}}^{\ensuremath{'}}}{{M}_{1}})]}^{\ensuremath{-}\frac{1}{2}}. \mathrm{Such}\mathrm{filters}}$ exhibit the same variations from theoretlcai performance as would be expected from a combination of the other two types. However, the agreement of each type with theory is sufficient to enable filters to be designed to fulfill set conditions. The attenuation secured with only four sections is very great, the transmission being certainly less than ${10}^{\ensuremath{-}7}$ in the attenuated region, while it may rise to 90 per cent. in unattenuated regions. Possible applications of these simple filters in laboratory work and in connection with specking devices, are briefly suggested.

Solubility of C O 2 and N 2 O in certain Solvents

Abstract: Solubility of $C{O}_{2}$ and ${N}_{2}O$ in Twelve Solvents, 18\ifmmode^\circ\else\textdegree\fi{} to 36\ifmmode^\circ\else\textdegree\fi{} $C$.---Since according to the Lewis-Langmuir theory these two gases have similar molecular structures, it is of interest to compare their solubilities in various liquids. In the method adopted, the air was thoroughly removed from the solvent by boiling and then the gas to be tested, having been carefully purified with the help of liquid air, was admitted and shaken up with the solvent until no further solution took place. Observations accurate to better than one per cent. were made for water, acetone, acetic acid, methyl alcohol, pyridine, ethyl alcohol, benzaldehyde, aniline, amyl acetate, ethylene bromide, isoamyl alcohol, and chloroform. Taken in this order, the ratio of the solubility of C${\mathrm{O}}_{2}$ to that of ${\mathrm{N}}_{2}$O decreases regularly from 1.34 (20\ifmmode^\circ\else\textdegree\fi{}) for water to 0.66 for chloroform. This range of variation is small, and moreover the ratio is nearly constant for each solvent, changing less than one per cent. for six solvents, and not more than three per cent. for the others except chloroform and acetone. Also, the temperature coefficient ($\frac{\mathrm{ds}}{\mathrm{sdT}}$) is in most cases nearly the same for the two gases. It is always negative, the solubility decreasing with increasing temperature.Discussion of Suggested Solubility Relations, for Gases in Liquids.---Raoult's law does not hold for the solubility of gases in liquids. It is also shown that there is little, if any, relation between solubility and the difference between the internal or cohesion pressures of solvent and solute. However, the ratio of the solubilities of C${\mathrm{O}}_{2}$ and ${\mathrm{N}}_{2}$O varies regularly with the dielectric constant of the solvent, and since this constant may be taken as an index of the polarity of the solvent and since C${\mathrm{O}}_{2}$ is more active chemically and therefore has stronger polarity than ${\mathrm{N}}_{2}$O, this result suggests that polarity may be an important factor in determining the relative solubility of gases in liquids.

The Sensibility of the Ear to Small Differences of Intensity and Frequency

Abstract: Intensity and pitch sensibilities of the ear as functions of loudness and frequency.---Intensity sensibility is defined, as usual, as the ratio of the least perceptible difference of energy to the total energy of that tone, $\frac{\ensuremath{\Delta}E}{E}$, while pitch sensibility is the ratio of the least perceptible difference of frequency to the frequency of the tone, $\frac{\ensuremath{\Delta}N}{N}$. There are considerable discrepancies among the results of previous investigators. The author used as a source of sound a telephone receiver actuated by a current from a vacuum tube oscillator. The intensity or the pitch could be changed periodically, once a second or so, by automatically changing the resistance or capacity in the oscillating circuit. The method of observation, then, was to change $\ensuremath{\Delta}E$ or $\ensuremath{\Delta}N$ continuously until the threshold of perception of fluctuation was reached. Separate observations usually checked within 10 per cent. As auxiliary experiments, in which the intensity was varied by changing the distance, showed that the acoustical energy of the source was a linear function of the electrical energy input, the latter was used as a convenient measure of the intensity of the sound. The frequency scale was determined by calibration. While the curves for the ears tested show individual differences, the results are in general the same for all. The intensity sensibility was found to be about 0.10 for moderate and high intensities but to increase to the limiting value 1 as the intensity decreases to the threshold. The curves are very similar to those obtained for the eye, and the modification of the Weber-Fechner law proposed by Nutting for light sensation also fits the results for audition satisfactorily: $\frac{\ensuremath{\Delta}E}{E}=F+(1\ensuremath{-}F){(\frac{{E}_{0}}{E})}^{n}$, where ${E}_{0}$ is the threshold intensity and $F$ is about 0.10. The exponent $n$ varies somewhat with the frequency, being 1.65 for 200 d.v. and 1.05 for 1,000 d.v.; nevertheless at the same loudness level, for instance 10,000 ${E}_{0}$, $\frac{\ensuremath{\Delta}E}{E}$ is nearly independent of frequency, showing only a 10 per cent. variation from 100 to 3,200 d.v. The results were the same whether harmonics were present or not. It is concluded that for 1,000 d.v. under favorable circumstances the normal ear can distinguish about 400 gradations of loudness between the threshold and a painful intensity ${10}^{12}$ times as loud. The pitch sensibility, $\frac{\ensuremath{\Delta}N}{N}$, was found to depend on relative loudness in nearly the same way as $\frac{\ensuremath{\Delta}E}{E}$. For the same loudness level, $\frac{\ensuremath{\Delta}N}{N}$ decreased from 0.01 at 50 d.v. to 0.003 at 600 d.v. and then remained constant up to 3,200 d.v. The limit of perception of variation of pitch was about the same or trained as for other ears, but training helped in distinguishing which note was higher. Two ears were found more sensitive than one ear to small differences of pitch but not to small differences of loudness.

Theory of Ionization by Cumulative Action and the Low Voltage Arc

Abstract: Theory of Ionization by Cumulative Action of Successive Impacts by Electrons and by Quanta of Resonance Radiation.---The phenomena of the low-voltage arc seem to require, for their explanation, ionization of the gas molecules in two (or more) successive stages. In the theory here developed it is supposed that each electron from the cathode after falling through a minimum potential difference reaches an active zone in which it collides either with a neutral molecule and partially ionizes it or with a partially ionized molecule which thereby becomes completely ionized. Each molecule when partially ionized emits a quantum of resonance radiation and this may go off in any direction and will in a short distance be absorbed by a neutral molecule which thereby becomes partially ionized and emits another quantum of radiation. So the passage through the gas of the quanta of resonance radiation initially set free by electronic impacts is analogous to the diffusion of foreign gas molecules. Equations for the case of coaxial cylindrical electrodes are derived for the proportion of molecules partially ionized (1) by direct impact and (2) by resonance radiation in terms of quantities which can all be readily measured except $\ensuremath{\tau}$ the mean life of the ionized molecules and $\frac{1}{\ensuremath{\rho}}$ the scattering coefficient for the radiation, for which (except $\ensuremath{\rho}$ for mercury) only upper and lower limits can be estimated. The substitution of experimentally determined values leads to the conclusion that, under normal circumstances, partial ionization by photo-impact is many times as great as that by electronic impact alone and is necessary and sufficient to account for the observed ionization. The possibility of complete ionization by successive photo-impacts alone is also discussed.Theory of Low-voltage Arc.---If ${n}_{0}$ is the number of electrons emitted and ${P}_{0}$ is the proportion of partially ionized molecules in the active zone, ${n}_{0}{P}_{0}$ is the number of molecules ionized per second. Since the positive ions move more slowly than electrons, each positive ion neutralizes the space charge due to $4\ensuremath{\surd}(2\ifmmode\times\else\texttimes\fi{}1840M)$ electrons; hence the electronic current increases to $\frac{1}{(1\ensuremath{-}242{P}_{0}\ensuremath{\surd}M)}$ times the value it would have without ionization, provided the current is limited by the space charge around the cathode. As ${P}_{0}$ is increased by increasing the temperature of the filament or the applied potential, the current first increases to the saturation thermionic current, then the negative space charge is replaced by a positive space charge, the potential drop becomes concentrated near the cathode, the temperature of the cathode is raised by bombardment by positive ions, increasing ${n}_{0}$ and hence ${P}_{0}$; as a result the current increases at an accelerated rate, instability is usually soon reached and the arc strikes suddenly. The chief function of the gas is to give the positive space charge around the cathode which is the distinguishing feature of the arc. If $n$ is the saturation value of thermionic emission, the maximum current will be $\frac{3}{2ne}$ or $2ne$ depending on whether the voltage is below or above the minimum ionizing potential.Low-voltage Arc in Mercury Vapor.---Recent experiments indicate that the striking voltage is about 5.6 instead of 4.9 volts, and that the arc may be dependent on either the 4.9 volt (2536 \AA{}.) or the 6.7 volt (1849 \AA{}.) radiation according to the age of the vapor. Thus there seem to be two meta-stable states of the neutral mercury atom.Theory of Temperature of Ionization of Gases.---It is pointed out that resonance radiation must also be the chief factor in temperature ionization both in the electric furnace and in the sun and other stars.

The Frequency—Sensitivity of Normal Ears

Abstract: Minimum Audible Pressure Variation for Tones of 60 to 4,000 Cycles.---The rather discordant results obtained by other investigators are briefly reviewed and are summarized in Fig. 1. In the present research an attempt was made to get results with a definite dynamical significance. A special air-damped telephone receiver held tightly to the ear, was excited by an alternating current of variable frequency from a vacuum tube oscillator provided with special low pass filters to eliminate upper harmonics, and the current strength was changed logarithmically by means of a special attenuator until the threshold was reached. The observations were made in a special sound proof room whose construction is described. The probable error is about 25 per cent. To reduce the results to absolute units, the system was calibrated in two ways, both involving the substitution of a condenser transmitter for the ear, the source of sound being a telephone receiver in one case and in the other a small thermal receiver inserted in the ear meatus or in a similar cavity in front of the condenser transmitter. Mechanical analogues of the vibrating systems involved in these measurements are described in an Appendix to help make the dynamics clear. While the unknown mechanical constants of the inner ear introduce some uncertainty, the agreement of the two calibrations indicates that the error is not large. Frequency-sensitivity curves were obtained for approximately 100 normal and 20 abnormal ears. So-called normal ears were found to vary widely in relative frequency sensitivity and in absolute sensitivity, and some audiograms show interesting individual peculiarities. But on the average, the minimum audible pressure variation increases regularly from about 0.15 dyne/${\mathrm{cm}.}^{2}$ at 60 cycles to 0.001 dyne/${\mathrm{cm}.}^{2}$ at 1,000 cycles and is then approximately constant up to at least 4,000 cycles.Variation of Sensitivity with Deafness.---People who require throughout the speech range (600 to 4,000 cycles) about 0.1 dyne/${\mathrm{cm}.}^{2}$ are called slightly deaf; those requiring 1 dyne/${\mathrm{cm}.}^{2}$ can still follow ordinary conversation; those requiring 10 dynes/${\mathrm{cm}.}^{2}$ need ear trumpets or other amplifying devices, and those requiring 1,000 dynes/${\mathrm{cm}.}^{2}$ are totally deaf.Attenuator for Varying the Current from an Oscillating Tube through Wide Ranges was constructed. It consists essentially of an artificial transmission line with resistance sections of series and shunt arms, so designed as to eliminate interfering effects between the various elements. The range of variation obtained is three million fold.

The Crystal Structure of Silver-Palladium and Silver-Gold Alloys

Abstract: Crystal Structure of Silver, Gold and Palladium and of Ag-Au and Ag-Pd Alloys.---Thin ribbons of the pure metals and of seven binary alloys of each series were prepared by fusing into small ingots and then swaging, drawing and rolling to thicknesses of from 1/400 to 1/200 cm. The x-ray diffraction patterns were photographed by allowing the K-radiation of Mo to fall for 8 to 20 hours on each ribbon. It was found that all these metals and alloys have their atoms arranged in face-centered cubic lattices. The parameter $a$ of each lattice, the edge of the cube, has the values 4.08 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}8}$, 4.075 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}8}$ and 3.90 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}8}$ cm. for pure Ag, Au and Pd respectively. For the Ag-Pd series, the parameter is nearly a linear function of the atomic per cent. of either component and this is also true for the Ag-Au series except that for the alloys with 30, 40 and 60 per cent. Ag the values of $a$ came out one per cent. too high. These results are for the most homogeneous and isotropic condition and are believed to be correct to within about 1/3 per cent. The effect of annealing at from 830 to 940\ifmmode^\circ\else\textdegree\fi{} C. for an hour or more in vacuo was to increase the size of individual crystals, to render them more homogeneous and to make their orientations more isotropic. The effect of moderate cold working, rolling, pressing or hammering is to reduce the size of the individual crystals and to make them less isotropic.Densities of crystals of silver, gold and palladium, computed from the above results of X-ray crystal analysis and the atomic weights, come out 10.49, 19.24 and 11.87 respectively. The Ag and Au were pure and the Pd contained only 0.5 per cent. impurity.

The Thermionic Work Function of Tungsten

Abstract: Measurements of the Thermionic Work Function of Pure Tungsten have been made by two methods for the same segment of a uniformly heated filament simultaneously. The filament, of diameter 0.0755 mm. and with three finer tungsten leads welded to it 3.85 cm. apart, was kept stretched, by means of a molybdenum spring, between two molybdenum plates used to apply an electric field and to receive the space current, the ends of the filament being surrounded by guard boxes to limit the emission to the section of the filament between the potential leads. All parts were sealed inside a tube and so thoroughly out-gassed by alternately baking the tube and heating the metal parts that the residual pressure during the measurements was only about ${10}^{\ensuremath{-}7}$ mm., as measured with an ionization manometer. (1) In the calorimetric method, the equivalent voltage of the work function was computed from the relation $\ensuremath{\phi}=\frac{2EI(\frac{\ensuremath{\Delta}E}{i})}{(E\ensuremath{-}\frac{\mathrm{IdE}}{\mathrm{dI}})}$, where $E$ is the voltage across the segment and $I$ the current through it, and $\ensuremath{\Delta}E$ is the voltage change when the space current $i$ flows from the filament, $I$ being kept constant. Since $\ensuremath{\Delta}E$ was only from ${10}^{\ensuremath{-}3}$ to ${10}^{\ensuremath{-}4}$ times $E$, special precautions had to be taken to measure it with sufficient accuracy and to keep $I$ sufficiently constant. Observations from 2070\ifmmode^\circ\else\textdegree\fi{} K. to 2300\ifmmode^\circ\else\textdegree\fi{} K. show an apparent increase for $\ensuremath{\phi}$ of about 2 per cent. in this range, considerably greater than is to be expected theoretically. At 2270\ifmmode^\circ\else\textdegree\fi{} K., when correction is made for the asymmetry of the electric shielding (- 2.24 per cent.) and for the radiation from the plates heated by the space current (+ 4.12 per cent.), $\ensuremath{\phi}$ comes out 4.91 \ifmmode\pm\else\textpm\fi{}.05 volts. (2) In the temperature variation method, assuming Richardson's equation $log i=\mathrm{const}.+\frac{1}{2} log T\ensuremath{-}\frac{\ensuremath{\phi}e}{\mathrm{kT}}$, measurements of the emission in the range 1930\ifmmode^\circ\else\textdegree\fi{} to 2300\ifmmode^\circ\else\textdegree\fi{} K. give for $\ensuremath{\phi}$ the values 4.87 or 4.78 volts according as the temperature scale of Langmuir or that of Worthing and Forsythe is adopted. The latter scale is probably more reliable but gives a value of $\ensuremath{\phi}$ 2.7 per cent. less than the value obtained calorimetrically, a difference believed to be greater than the probable error of the measurements.Suggested Modification of the Theory of Conduction of Electricity in Metals.---The thermal energy of conduction electrons is supposed to be $\frac{3}{2kT}$ by the classical theory upon which the above computations of $\ensuremath{\phi}$ are based. If, however, the energy is taken to be practically zero then the same data lead to 4.52 and 4.48 volts for the values of $\ensuremath{\phi}$ by the two methods and the agreement is within the probable error of the measurements.

The Sensitivity and Precision of the Electrostatic Transmitter for Measuring Sound Intensities

Abstract: Electrostatic Transmitter of Constant Sensitivity.---(1) Characteristics. This instrument is the same in principle as that described in 1917, but certain changes have been made which, as proved by actual tests, render the sensitivity independent of changes of temperature, pressure and humidity. The sensitivity is also found to be constant over a long period of time. By means of a piston-phone and a thermophone, for which corrected formul\ae{} are available, both the absolute sensitivity and phase lag were determined for frequencies of from 10 to 12,000 cycles. Eight transmitters similarly constructed give the same curves within 20 per cent. With a steel diaphragm 0.0051 cm. thick having a natural frequency of 7.000 cycles, and with an air gap of 0.0025 cm., the mean sensitivity is about 0.35 millivolt/dyne. (2) Use with an amplifier for measurement of sound intensity. Combined with an amplifier of ordinary design the instrument has an over-all sensitivity which is practically uniform from 25 to 8,000 cycles. It is therefore remarkably well adapted for the measurement of the intensities of complex tones and tones of changing pitch and for use with an oscillograph for recording sound waves. On the other hand, if sounds of a definite pitch are to be measured, the apparatus can be made highly selective and almost any desired sensitivity can be obtained by using a tuned amplifier in connection with a vibration galvanometer.

Spectra of Hydrogen, Nitrogen and Oxygen in the Extreme Ultraviolet.

Abstract: Spectroscopy of Extreme Ultraviolet.---A method which has been developed of coating films with an emulsion suitable for work in this region is described in detail, and also an oil-cooled discharge tube of the internal capillary type which will stand an input of 2.25 KW and thus reduce the time of exposure and consequent fogging of the films from 10 to 100 fold. Transparency of oxygen, nitrogen and air between 500 and 1,800 \AA{}. was investigated. In a vacuum spectrograph with a grating of 50 cm. radius these gases were found to transmit light of from 1100 to 1225 \AA{}. even when at a pressure of 3 cm. At around 1 mm. spectrum lines were photographed from 800 to 1,800 \AA{}. and with oxygen at 0.001 mm., the spectrum was photographed to 430 \AA{}. These gases, then, are not as opaque to light in this region of the spectrum as has been generally supposed.Spectrum of discharge through hydrogen, 1,220 to 885 \AA{}. The ultraviolet limit is the same for both continuous and disruptive discharges. Four spectrograms are reproduced and the wave-lengths are given for 90 lines below 1,059 \AA{}., presumably due to hydrogen, as a continuous stream of pure gas was supplied. The resonance line was found superimposed in the fourth order on the ${\mathrm{H}}_{\ensuremath{\beta}}$ line; hence its wavelength is 1,215.68 \ifmmode\pm\else\textpm\fi{} 0.03 \AA{}. This coincidence confirms the Bohr formula for this line, which is the first of the Lyman series.Spectrum of Discharge through Nitrogen, 1,750 to 835 \AA{}.---The continuous discharge gives chiefly the band spectrum of nitrogen, which is extended to 1,026 \AA{}., the wave-lengths of 19 bands below 1,385 \AA{}A. being given. The wave-lengths of 50 new lines obtained with the disruptive discharge are also given and four spectrograms are reproduced.Spectrum of Discharge through Oxygen, 1,863 to 507 \AA{}.---Wave-lengths of about 100 new lines obtained with a disruptive discharge are given and six spectrograms are reproduced. When mercury vapor was present about 15 additional lines extending to 433 \AA{}. were obtained.Explanation of fluorescence observed around aluminum spark in air by Lenard in 1910, to a distance of 4 cm., may depend on the transparency of air to light of wave-length 1,000 to 1,400 \AA{}.

The Crystal Structure of Quartz

Abstract: The Structure of Quartz (Si${O}_{2}$).---By means of the Lewis theory, a structure has been obtained for quartz which accounts in a satisfactory way for the crystalline form, crystal symmetry, optical rotation, hardness, high melting point, insolubility, and x-ray spectra of the substance. It is in strict accord with the conclusions of W. H. Bragg in regard to the structure. Furthermore, the distance between adjacent silicon and oxygen atoms, calculated from the dimensions of the lattice, as obtained by Bragg, is approximately equal to the sum of their atomic radii, obtained from other crystals.The Arrangement of Atoms and Electrons.---Each silicon atom is surrounded by four pairs of electrons at tetrahedron corners, which act as bonds connecting it to four equidistant oxygen atoms. Each oxygen atom is also surrounded by four tetrahedrally oriented electronpairs, two of which serve as bonds connecting the oxygen to silicon atoms. The crystal is thus not made up of Si${O}_{2}$ units, but is a single molecule, for all of the bonds around each silicon or each oxygen atom are of the same type---the usual type of bond which connects the atoms in a molecule.

Bombardment of Metal Surfaces by Slow-Moving Electrons

Abstract: Secondary Electrons Produced by Electronic Bombardment of Nickel.---The main features of the apparatus used are: an equi-potential nitrate-coated Pt cathode heated by radiation from a tungsten spiral filament; a series of insulated diaphragms to limit the beam of primary rays and for use in determining their velocity; and a long Faraday cylinder in front of which the nickel target could be alternately interposed and withdrawn. By baking out the tube and using liquid air traps an extremely low vacuum corresponding to less than ${10}^{\ensuremath{-}7}$ mm. was attained. The secondary current was determined from the difference between the current to the Faraday cylinder and that to the interposed target. (I) Ratio of the secondary (emergent) to the primary (incident) electron current was found to be independent of the roughness of the surface, but to vary with the treatment. After heating the target red-hot by high frequency induction for some minutes, a limiting curve was reached which probably represents the characteristics of nickel itself, free from surface contamination. In this case the secondary electrons begin when the primary velocity is as low as 0.2 volt; the ratio to primary current then increases rapidly with primary velocity to about 4 volts, remains constant to about 9 volts, then again increases reaching a value of unity for a primary velocity corresponding to about 260 volts. The effect of exposure to air or hydrogen is to increase very considerably the secondary current and to round out the flat part of the curve between 4 and 9 volts. (2) Velocity distribution curves of the secondary electrons indicate that for primary electrons of less than 9 volts velocity, most of the secondary electrons have velocities nearly equal to the primary velocity, while for primary velocities above 9 volts, the percentage of secondary electrons having small velocities increases with the primary velocity, although a small proportion have velocities nearly equal to the primary velocity up to at least 110 volts.Reflection and Emission of Electrons from a Nickel Surface Bombarded with Electrons of Velocity 0 to 260 Volts.---It is suggested by the above results, that reflection occurs for all the primary velocities investigated, and that emission or ionization begins at about 9 volts and increases with the primary velocity.Contact difference of potential between a gas-free nickel surface and an ordinary baked nickel surface was found to be 0.8 volt.Method of making a gas-tight glass joint for high vacuum work by soldering with Wood's metal, the platinized and copper-coated surfaces of a ground joint, is described.

Analysis of the Energy Distribution in Speech

Abstract: The frequency distribution of energy in speech has been determined for six speakers, four men and two women, for a 50-syllable sentence of connected speech, and also for a list of 50 disconnected syllables. The speech was received by a condenser transmitter whose voltage output, amplified 3,000 fold, was impressed on the grids of twin single stage amplifiers. The unmodified output of one of these amplifiers was measured by a thermocouple and was a known function of the total energy received by the transmitter, corrections being made for the slight variation with frequency of the response of the circuit. The output of the other amplifier was limited by a series resonant circuit to a narrow band of frequencies, the energy in this band being measured by a second thermocouple. The damping of the resonant circuit was so chosen that sufficient resolving power and sufficient energy-sensitiveness were obtained over the range from 75 to 5,000 cycles per second; and 23 frequency settings were made to cover this range. For each syllable simultaneous readings were recorded on the two thermocouples at each frequency setting. The consecutive syllables were pronounced deliberately by each speaker, maintaining as nearly as possible the normal modulation of the voice. Corrections were applied to offset the unavoidable variations in total energy incidental to repetition of a given syllable. 13,800 observations were made for all speakers. The energy distribution curves obtained are essentially the same for connected as for disconnected speech, and indicate that differences between individuals are more important than variations due to the particular test material chosen. A composite curve drawn from the individual curves shows a great concentration of speech energy in the low frequencies, a result which would not be expected from data previously published by others. The actual results contain a factor due to standing waves between the speaker's mouth and the transmitter, a complication always present in telephoning; this could not be eliminated.The rate of energy output in speech for the normally modulated voice, was determined from the readings for total energy and was found to be about 125 ergs per second.

Reciprocal Diffraction Relations between Circular and Elliptical Plates

Abstract: Diffraction Patterns inside Elliptical Shadows Due to a Point Source of Light.\char22{}When a circular disc with its plane originally tangent to the light wave is rotated about an axis in its plane, the Arago spot changes to a figure with four cusps which move out along the axes of the elliptical shadow, two approaching the foci as limits and the other two going outside the shadow. These changes are shown by a set of photographs obtained with a disc 1.6 cm. diameter placed 2 meters from a pinhole 0.3 mm. in diameter and 5 meters from the photographic plate. The diffraction pattern was found to depend only on the ellipticity of the shadow whether produced by an ellipse or by an inclined disc. Each quadrant of the diffraction pattern was found to be associated with the quadrant of the shadow adjacent to it but on the opposite side of the major axis. Careful measurements of the photographs proves that in each case the diffraction pattern is the evolute of the geometrical shadow. The effect is as though each element of the edge of the shadow contributed a spot along its normal, the result being a caustic curve of diffraction.

The Mobility of Electrons in Pure Nitrogen

Abstract: Mobility of electrons in pure nitrogen was determined, using the Rutherford alternating potential method, for pressures ranging from $75 \mathrm{to} 600$ mm., for frequencies ranging from $7,000 \mathrm{to} 150,000$ cycles (obtained from an audion oscillating circuit), and with electric fields of from 10 to 100 volts/cm. Reduced to atmospheric pressure the mobility found is of the order of 10,000\ifmmode\cdot\else\textperiodcentered\fi{} cm. sec.,/many times the highest value previously obtained, and it was observed to vary with pressure and electric field according to the equation $K=\frac{571,000}{(21+760 \frac{V}{\mathrm{pd}})}$, where $\frac{V}{d}$ is in volts/cm. and $p$ in mm. of Hg. A discussion of the possible sources of error shows that none can be responsible for this variation with $\frac{V}{\mathrm{pd}}$, and the form of the mobility curves confirms this variation. A theoretical interpretation of these results on the basis of the Townsend equation for electron mobility leads to the conclusions: that if the Townsend theory is correct (1) either the energy lost at each impact of an electron with a nitrogen molecule or the mean free path must be a function of $\frac{V}{\mathrm{pd}}$, and (2) in either case the mean free path for velocities of the normal agitation must be about 22 times the mean free path of the gas molecules instead of $4 \sqrt{2}$ times, as given by the kinetic theory.

An Extension of the Principle of the Diffraction Evolute, and Some of its Structural Detail

Abstract: Diffraction Patterns inside Shadows due to Point Sources of Light---(1) Conic section shadows In confirmation and continuation of the results in the preceding article, the patterns are found to depend only on the shape of the shadow, the Arago spot being obtained at the center of the circular shadow even when this was cast by a spiral edge of large pitch ground to the form of a truncated cone, when the point source was placed at the apex Patterns inside the shadows of hyperbolic and parabolic plates were also obtained and are reproduced As in the case of the ellipse, the predominant figure in each case is the evolute of the edge of the shadow (2) This general relation between diffraction caustic and shadow is found to hold even in the case of the shadow of the involute of a circle, when the diffraction figure was identical with the generating circle which was, of course, the evolute of the edge of the shadow A series of photographs of elliptical shadows show that the diffraction caustics are not continuous curves The changes of detail and of color in the patterns with change of ellipticity of the shadow are described at some length

The Dielectric Constant of Mica

Abstract: Dielectric Constant of Mica.---The constant was determined for 18 samples of mica, varying in thickness from 0.005 to 0.073 inch and including 12 different grades. Each sheet was placed between two mercury electrodes and the capacity of the condenser thus formed was determined with a shielded capacity and conductance bridge using alternating current at 1,000 cycles per second. It was found that while thick sheets with plainly visible air films had low dielectric constants, those without such films gave fairly consistent results, running from 6.4 to 9.3 with an average of 8.1. When a thick sheet was split, the thinner sheets had higher constants except in the case of a sample of Canadian amber.Power Loss in Mica Condensers was too small to determine accurately with the apparatus used, but was higher for stained than for clear micas.

The Crystal Structures of Marcasite (Fe S 2 ), Arsenopyrite ( FeAsS ) and Loellingite (Fe As 2 )

Abstract: The Structure of Marcasite.---An arrangement of atoms and valence electrons, which is consistent with all known experimental facts, is proposed for marcasite (Fe${\mathrm{S}}_{2}$). The arrangement around each atom is very similar to that in pyrite. The sulfur atoms are in pairs. Each sulfur is bonded, by pairs of electrons, to one sulfur and four iron atoms, and each iron atom to six sulfur atoms. Taking the unit distance from the dimensions of the pyrite structure, the density is computed, the value obtained being the same as that experimentally observed, within the limits of experimental error. The distortions of the atoms in the structure are discussed.The Structures of Arsenopyrite (FeAsS) and Loellingite (Fe${\mathrm{As}}_{2}$).---Assuming the same general arrangement for arsenopyrite and loellingite as for marcasite, the dimensions of the unit cells are obtained, and these compared with those of marcasite.

A New Tone Generator

Abstract: New Pure Tone Generator and Receiver of Sounds.---(1) Construction and operation. The instrument consists of a thin, non-magnetic, metallic diaphragm between two flat coils through which a constant direct current ${I}_{0}$ flows in such a way as to produce a radial magnetic field in the diaphragm; then when a simple harmonic alternating current $I$ of the frequency $\frac{\ensuremath{\omega}}{2\ensuremath{\pi}}$ is superposed upon the direct current, circular currents are induced in the diaphragm, which thereupon is acted upon by a simple harmonic electrodynamic force and vibrates with the frequency of the alternating current. For low frequencies the electrodynamic force is approximately proportional to $\ensuremath{\omega}{I}_{0}I sin (\ensuremath{\omega}t+\ensuremath{\theta})$ and the amplitude of vibration is approximately proportional to $\frac{{I}_{0}I}{\ensuremath{\omega}}$. The absence of overtones is due to the absence of ferromagnetic material, and to the fact that the radial magnetic field is constant. The aperiodicity of the diaphragm renders the calculation of the performance of the instrument practicable, and eliminates distorsion, due to resonance, in the wave form of the emitted sound when the instrument is excited by a complex alternating current. When used as a generator of pure tones, the coils were connected in the circuit of a thermionic oscillator whose frequency could be varied from 500 to 25,000 vibrations per second. When used as a receiver of sound, the current generated in the coils by the motion of the diaphragm is fed into a thermionic amplifier. (2) Quantitative study of the performance. The distribution of the magnetic field between the coils was determined experimentally; the diaphragm current equations were deduced and solved for a particular case; the forces on various parts of the diaphragm were calculated, and thence the amplitude of vibration and the sound energy output. With an aluminum diaphragm 0.0025 cm. thick and 10 cm. in diameter, a direct current of 1 ampere, an alternating current of 0.085 ampere, and a frequency of $\frac{{10}^{5}}{2\ensuremath{\pi}}$, these were respectively 7 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}7}$ cm., and 9 ergs per second. By increasing both direct and alternating currents five-fold, the output could be increased over six hundred-fold. Measurements of the amplitude for various frequencies agreed well with the calculated values. (3) Applications of the instrument. Since it gives a pure tone of constant and measurable pitch and intensity over a wide range, it would serve as a precision source of sound, useful both for research and lecture purposes. When used as a telephone receiver and transmitter, actual tests have shown that the reproduction of sound is remarkably faithful.