Index of content:
Volume 19, Issue 11, 01 November 1948

Velocity of the Anode Spark in Copper Sulfate Solutions Under Application of Impulsive Potential
View Description Hide DescriptionThe velocity of the luminous anodespark produced in CuSO_{4} solutions by application of impulsive potential has been measured as a function of the interelectrode gap, input voltage, and solution normality. Determinations were made for input potentials of 15–30 kv, interelectrode gaps of 15–80 mm, and solution concentrations of 0.0125–0.0625N.
The spark velocity was found to depend upon the input potential and the interelectrode gap by the empirical equation:where V is the spark velocity in meters/sec., E _{0} is the input voltage in kv, and G is the interelectrode gap in cm. Qualitatively, it was observed that as the solution normality increased, the maximum breakdown distance decreased and the spark behaved more erratically.
The maximum length which the spark streamers reach may be stated empirically by the equation:where L_{m} is the maximum streamer length in cm, E _{0} is the input potential in kv, G is the interelectrode gap in cm, and N is the normality of the solution.
The computed potential at which the spark cases its progress through the liquid, E_{m} , was found to be proportional to the input potential but independent of the interelectrode gap and the solution concentration. The ratio E_{m}/E _{0} was 0.646. The time lag in initiation of the spark was also found to depend upon the input voltage but to be independent of the interelectrode gap and the solution concentration.

Bidwell's Intercept Relation and the Thermal Conductivity of Liquid Metals
View Description Hide DescriptionA note pointing out that the claim made by Bidwell and Hogan [Journal of Applied Physics 18, 776 (1947)], that the relation k/ρC=K(1/T)+K ^{1}, where k is the thermal conductivity, ρ the density, C the specific heat, T the absolute temperature and K and K ^{1} are constants, holds for aluminium,tin,lead and zinc with the intercept, K ^{1}, the same for the solid and liquid phase, is not so well supported by experimental evidence as the reader is led to believe.
The latest paper on aluminium makes no reference to Konno's appreciably different results for the thermal conductivity of liquidaluminium. Furthermore, adjustment appears necessary in the plotting of Bidwell and Hogan's two points for the liquid phase and this brings the intercept for the liquid phase about 30 percent above that for the solid phase.
Of the other three metals cited by Bidwell and Hogan as having been previously shown to conform to the intercept relationship, it is revealed that zinc does not on the experimental evidence of both Bidwell and Konno, lead does on the evidence of Bidwell but not on that of Konno, whilst tin does on the evidence of Konno only. Further experimental investigation is clearly necessary before any definite relationship such as that suggested can be accepted.

The Effective ``Gamma'' for Isentropic Expansions of Real Gases
View Description Hide DescriptionIn an isentropic expansion of a real gas, the relationship pv ^{γ} = C (γ, C constant) is not exact. A development is given for an accurate exponent ᾱ (the effective ``gamma''), related to the ratio of specific heats, which permits the use of the relationship p _{0} v _{0} ^{ᾱ} = p _{1} v _{1} ^{ᾱ} for an isentropic expansion between any two pressures. The exponent may be computed from the initial conditions of the gas, the expansion ratio, equation of state data, and data on the variation of specific heat with temperature.

On the Mixing Properties of Non‐Linear Condensers
View Description Hide DescriptionThe theory of a mixer circuit, containing a non‐linear condenser as a mixing element, is developed. It is shown that such a condenser has an imaginary conversion transconductance and a capacitive input and output impedance. It is found that the circuit has widely different properties, depending upon the choice of the frequency, ω_{ m }, of the local oscillator, the i‐f frequency, ω_{0}, and the input frequency, ω_{ i }. The following three cases are considered: (a) ω_{ m } = ω_{ i }+ω_{0}, (b) ω_{ m } = ω_{ i }−ω_{0}, and (c) ω_{ m } = ω_{0}−ω_{ i }. A non‐linear condenser in a mixing circuit acts as a transformer; in the cases (b) and (c) the mixing condenser transforms an i‐f impedance into a positive input load; in case (a) an i‐f impedance is transformed into a negative input load, so that oscillations may even occur. In case (c) the power gain is larger than unity, the power delivered to the circuit by the antenna is smaller than the power dissipated by the output load, and the difference is due to the power delivered by the local oscillator. In case (b) the power gain is smaller than unity, because in this case power is dissipated by the local oscillator. In case (c) instability may occur; the circuit is then capable of splitting the local‐oscillator signal into two signals of frequencies, ω_{ i } and ω_{0}, respectively. The band width and the noise factor of the circuit are also discussed; it is shown that the circuit might have a very low noise factor. A few experiments are given which show qualitative agreement with theory.

An Extension of Lagrange's Equations to Electromagnetic Field Problems
View Description Hide DescriptionThis paper contains the basic theory of an extension of Lagrange's equations which renders these equations and the procedures associated with them in mechanics applicable to electromagnetic field problems such as are encountered in ultra high frequency work and other branches of engineering. In certain important cases the Lagrangean procedures so obtained give equivalent networks. Successful applications of these procedures to several practical problems are indicated.

An Observation on Heat Sources Placed at Random on a Surface
View Description Hide DescriptionA mean value theorem and a fluctuation theorem are derived for the case where a potential is due to sources of potential placed irregularly on a surface. The purpose of the theorems is to provide a check on theories of solid‐solid friction where extremely high ``local temperatures'' are sometimes assumed. The result indicates that a certain caution should be exercised in using such concepts.

Wave Guides for Slow Waves
View Description Hide DescriptionThe paper is devoted to a discussion of the properties of electromagnetic waves propagating with a velocity W <c. Boundary conditions are obtained for structures with very narrow slots, either closed or open, and a general method of solution of the wave equations is discussed. Fields in the free region and in the slot region are expanded in convenient Fourier series and these series joined along the border of both regions. In doing this, it can be proved that the field contains a dominant term, completed by corrections that represent the field distortion near the open end of the slots. Under favorable conditions, and for very narrow slots, the dominant terms are by far the most important. This allows for a simplified discussion of a variety of examples. The results obtained are in agreement with those of E. L. Chu and W. W. Hansen (J. App. Phys. 18, 996 (1947)).

Divergent Beam X‐Ray Photography with Standard Diffraction Equipment
View Description Hide DescriptionA new method for preparing divergent beam x‐ray photographs of crystals is presented. This employs the usual Laue transmission camera and a collimated primary beam of x‐rays. Fluorescent radiation originating either in the crystal sample or at a radiator in front of the crystal is used as the source of divergent x‐rays. Some applications of the technique to determinations of orientation, lattice parameters, and crystal perfection are illustrated.

An Ion Microscope with a Transverse Magnetic Field
View Description Hide DescriptionA brief discussion of electron and ion microscopes is presented followed by a description of a low magnification, electrostaticion microscope. This instrument is of the emission type wherein the source of positive ions is imaged. If more than one species of ion is emitted, the images corresponding to the various atom weights may be separated by means of a transverse magnetic field and the ratio of atomic weights calculated from the displacements. The possible uses of such an instrument are pointed out.

Growth of Charged Particles in Clouds
View Description Hide DescriptionIn order to calculate the average growth of a charged particle in a dust cloud caused by electrostatic attraction, the following assumptions were made: the particles obey Stokes' law of motion, their velocities are small so that their motion can be considered to be in constant equilibrium with the forces acting, and the forces are effective at short ranges only or the cloud density is small enough so that not more than two particles have to be considered interacting at a time. In addition to the Coulomb force, there will appear an attraction between particles resulting from induced dipoles, but it was found that in general the effect of this force can be neglected. Straight forward integration of the equation of relative motion of two charged dust particles yields their effective cross section for aggregation from which in turn we can determine the rate of growth if the particle size and charge distribution in the cloud is known. Assuming a highly simplified distribution, one arrives at the result that aggregation is negligible if the cloud density is less than a million particles per cm^{3} or if the average charge of one sign is well below a thousand electrons per particle.

Magnitude and Character of Errors Produced by Shape Factors in Stokes' Law Estimates of Particle Radius
View Description Hide DescriptionIn order to estimate the possible errors introduced by deviations from the spherical particle shape in Stokes' law estimates of dust particle sizes, a model study was made with objects of various shapes falling in oil of high viscosity. It was found that all shapes fall more slowly than the sphere of the same mass and volume. The true size and mass will, therefore, always be larger than the estimates calculated from their rate of fall by means of Stokes' law. For shapes of extreme dimensions (very thin plates and needles) the error thus introduced exceeded 50 percent. For more common configurations of spheres it was of the order of 20 percent or less. No simple relation between particle surface or any other parameter and the rate of fall could be discovered. All plates and needles turned their planes and longer axes into a horizontal direction when falling freely, unless one side was distinctly weighted. A small asymmetry in weight distribution tilts the planes slightly, causing the model to drift sideways in its fall. In a Hopper and Laby method of particle analysis such a drift makes a particle appear charged, although it may be neutral. It is, therefore, not possible to analyze platelike and needlelike powder and dust particles by such a method.

On the Measurement of Cavity Impedance
View Description Hide DescriptionA method of measuring cavity impedance is described.

The Fracture of Liquids
View Description Hide DescriptionA liquid subjected to negative pressure is metastable; vapor bubbles form spontaneously and grow until the pressure of the system rises to the equilibrium vapor pressure. The rate of bubble formation is calculated from the theory of nucleation, and the negative pressurep_{t} that gives one bubble (i.e., fracture) in t seconds is determined. p_{t} is very nearly independent of t, and is proportional to where σ is the surface tension. Subcooled liquids such as glass also are metastable under negative pressure;cracks form spontaneously and grow until the pressure rises to the equilibrium vapor pressure.Nucleationtheory leads to an expression for the fracture stress of glass that is proportional to (E ^{2}σ^{3})^{¼} where E is the elastic modulus. The transition from high temperature cavity‐nucleated fracture to low temperature crack‐nucleated fracture is examined.
Fracture strengths calculated from nucleationtheory agree satisfactorily with the maximum experimental values, and are an order of magnitude smaller than the forces required for simultaneous separation of all atomic bonds cut by a plane surface. The frequent occurrence of premature failure is associated with the presence of pre‐existing surfacecracks in glass, and of positive contact‐angle impurity in contact with liquids.

Geometrical Factors Affecting the Contours of X‐Ray Spectrometer Maxima. I. Factors Causing Asymmetry
View Description Hide DescriptionThe observed asymmetry of x‐ray spectrometer maxima arises principally from three‐dimensional properties of the ideally two‐dimensional focusing arrangement employed, vertical divergence of the primary beam being the fundamental cause. A mathematical formula is developed that expresses the degree of asymmetry as a function of the reflection angle and the geometrical properties of the apparatus. The asymmetrical effects predicted in this way are qualitatively confirmed with experimental measurements. Practical suggestions are made for minimizing asymmetry.

Theory of the Positive Column in an Annular Discharge Tube
View Description Hide DescriptionOn the ground of Schottky'sdiffusiontheory of the positive column, the distribution of the electron and ion concentration and of the current density in an annular discharge tube are calculated.

Electron Diffraction Study of Particle Size in Thin Bi Films Deposited by Evaporation in Vacuum
View Description Hide DescriptionElectron diffraction patterns of thin Bi films were studied by the method of microphotometer density curve analysis to determine changes of the filmstructure with aging and with increase in thickness of the films. All Bi films were deposited on Formvar by evaporation in vacuum. Analysis of the Bi diffraction patterns by comparison with the Formvar pattern as a reference standard indicate that the very thin films (about 20 atom layers or less in thickness) while initially composed of small crystals grow rapidly upon aging into larger crystals. The very thinnest film (about 5 atom layers thick) analyzed exhibited an initial increase in particle size followed by a decrease upon aging, a somewhat anomalous result requiring further confirmation.
Increase in particle size with increase in thickness of the Bi films is observed also, although the results of these latter experiments are somewhat irregular.

Plastic Flow, Creep, and Stress Relaxation. Part IV. Anomalous Flow as an Order‐Disorder Transition
View Description Hide DescriptionPlastic systems show effects of steric hindrance at rest, which results in a molecule preventing its neighbors from occupying certain positions and introduces a certain degree of orientation. Under stress many more positions, resulting from the rotation, are forbidden to a molecule in motion. In order to make more positions available, the system must increase its volume under stress and changes from a state of greater order to a state of greater disorder. Based on this concept equations are given which present the strain‐rate at constant temperatures as functions of stress, change in volume and degree of order and disorder. The changes in entropy and energy of interaction, accompanying the strained state, are expressed by a generalized partition function. This concept of anomalous flow is extended to visco‐elastic effects for systems with rubber‐like elasticity, and has been exemplified by data on polychloroprene under tension.

Note on ``Statistical Aspects of Fracture Problems''
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Transmission Properties of Materials in the Millimeter Wave Region
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