Index of content:
Volume 21, Issue 11, 01 November 1950

On Crazing of Linear High Polymers
View Description Hide DescriptionThe effect of various variables, such as type of stress, stress magnitude, duration of stressing, and environment on the initiation and development of crazing in linear polymers is discussed. The basic nature of crazing is investigated in some detail for polystyrene specimens by means of the light microscope, the electron microscope and the x‐ray spectrometer. The results of these observations and their bearing on the fundamental group structure of polystyrene molecules is presented.
The relationship between crazing and orientation is discussed, as well as the effect of both of these factors on the mechanical properties. The experimental results are compared, wherever possible, with the previously reported data of other investigators. A short discussion is then given of a theory of crazing from the point of view of the molecular structure of the material.

End‐Cooling of Power Tube Filaments
View Description Hide DescriptionThe differential equation defining the relation between temperature and distance in that portion of a vacuum tube filament which is cooled by both conduction and radiation is formulated. This equation has been solved by numerical integration; the results are presented as a set of universal curves in a form convenient for use in vacuum tube design. The calculations agree well with some experimental measurements which were made to verify the theory.

Space‐Charge Effects in Electron Beams and Their Reduction by Positive Ion Trapping
View Description Hide DescriptionThe spread of electron beams caused by space‐charge forces is discussed. Under certain conditions ions formed from the residual gas may be trapped in the beam. An equilibrium condition may be established in which the electron and ion densities are equal, and then space‐charge forces will be neutralized. Under these conditions high current densities may be produced at low voltages. A theory of ion trapping is discussed, and the equilibrium condition is formulated.
Experimental data are presented which were obtained by the application of microsecond pulses to the beam. This technique is described, and its advantages and possibilities are mentioned. Data are given on beam spread as a function of current, voltage and pressure. Data on the improvement due to ion trapping are included. An increase of current density by a factor of 30 was observed with the structures tested. Results are included on ion build‐up time as a function of pressure, and on beam noise and stability in the presence of trapped ions.

Stress‐Strain Properties of Natural Rubber under Biaxial Strain
View Description Hide DescriptionTube‐shaped samples were stretched in a direction parallel to the tube axis and at the same time inflated to cause a tangential extension. In this way 600 percent axial and 300 percent tangential elongation could be attained simultaneously. The stresses were calculated from the pressure in the tube and the dynamometer readings.
The results are plotted as axial stress‐strain curves at different tangential elongations ranging from 0–300 percent.
The curve for a higher tangential elongation lies at higher stresses than that for a lower tangential elongation; the differences are however larger than the theory predicts.
At 600 percent axial elongation stress relaxation was measured at different tangential elongations. It appears that the relaxation constant is independent of the tangential elongation.

On the Endurance Limit of a Round Bar with Longitudinal Grooves
View Description Hide DescriptionIn a previous paper, we reached a consideration that the endurance limit of a material should be determined by the amount of the mean stress in a certain area around a point, instead of the stress at the point, and the extent of the area is determined for several kind of metals, by using the results of tension‐compression fatigue tests.
In this paper, the extent of area where the mean value of stress to be taken, is determined for a mild steel in another way, viz., by a torsion fatigue test, and we reached the conclusion that the extent of area chiefly depends on the kind of metal and independent of the course of the experiment.

The Magnetic Field of a Plane Circular Loop
View Description Hide DescriptionThe axial and radial components of the magnetic field of a plane circular loop are expressed in terms of cylindrical coordinates. The expressions involve two integrals which are related to certain of the complete elliptic integrals. Tables of values of these integrals are presented. Interpolation in these tables facilitates rapid calculation of the field components.

Effect of Coating Composition of Oxide‐Coated Cathodes on Electron Emission
View Description Hide DescriptionInvestigation of oxide‐coated cathodes has been made to determine the effect on electron emission of varying the proportions of emitting oxides. The results show that maximum electron emission under saturation conditions is obtained from a solid solution containing strontium oxide (SrO) and barium oxide (BaO) in an approximate molecular ratio of 7 to 3.
These results also indicate that maximum size of the co‐precipitated alkaline‐earth carbonate particle occurs at the same molecular ratio as that giving maximum electron emission from the oxides.
When the saturation emission obtained with a square‐wave voltage pulse was measured, the current pulse as observed on a synchroscope was also a square wave and showed no measurable decay characteristic for a pulse duration time of 10 microseconds.

Surface Waves and Their Application to Transmission Lines
View Description Hide DescriptionIn this paper the applicability of non‐radiating surface waves for transmission lines is investigated. Two types of waves are considered. The first one, originally studied by A. Sommerfeld, is guided by a cylindrical conductor of finite conductivity. Although this wave type has (under comparable conditions) much lower attenuation than the waves in coaxial cables or rigid wave guides, its practical application is restricted by the fact that the extension of the field is very large. Efficient excitation and undisturbed propagation of this wave mode are feasible only for very high frequencies. The other wave type considered in this paper has not been treated in the literature. It is guided by a conductor which is coated with a dielectric layer or the surface of which is otherwise modified; for example, by being threaded. The field of this wave type has a structure similar to that of Sommerfeld's wave, but the extension of the field can be controlled by the surface modification. Thus low loss transmission lines on the basis of this wave type become feasible for frequencies above 100 megacycles. The information necessary for the design of such lines is given and the agreement between the theoretically expected transmission losses and the measured transmission losses is checked.

A Note on Control Area
View Description Hide DescriptionControl area, or the integrated error for a step function input, has been used as a measure of control system performance. For systems described by , it is proved that the control area is . A simple method of evaluation is presented and some limitations of the control area criterion are mentioned.

A Small Electron Microscope
View Description Hide DescriptionA new electron microscope of greatly simplified design has been constructed. The instrument has a resolution of 100 Angstroms, yet is small enough to be mounted on a desk or laboratory table. Magnetic lenses are energized by permanent magnets. An accelerating voltage of 50 kilovolts is varied over a narrow range to provide means of focus. Images may be photographed on 2×2 plates. Plates may be changed in a minute, and specimens in fifteen seconds. Direct magnifications of 1500, 3000 and 6000 are possible depending on pole pieces used. Photographic images may be enlarged up to ten times. The instrument is free of x‐radiation and completely interlocked and provided with shorting devices for protection from high voltage.

Artificial Field Equations for a Region Where μ and ε Vary with Position
View Description Hide DescriptionI. Theory. The field equations developed admit of solutions in regions where μ and ε vary with position. For regions of zero conductivity, they are symmetrical with respect to electric and magnetic quantities, and the TM case can be derived from the TE. Fields derivable from a single component 4‐potential are examined, and their propagation equations are found. A table relates the tensor and pseudo‐tensor components to the usual vector components.
II. Applications in cylindrical polar coordinates. For the TE case, three types of solution exist, called A, B, or C, where the E field is parallel to the elementary vectors dz, dr or rdθ, respectively (for the TM case, H replaces E). In each TM or TE case, two possible distributions of μ and ε occur, leading to separable propagation equations. TEMwaves can be derived from both TM and TE cases, but the impedances are different.
TE, TM and TEMwaves for certain specific distributions of μ and ε, and their applications to curved guides, horns, and co‐axial lines are considered. Some expressions are obtained for the fields, propagation constants, cut‐off frequencies, and impedance. These solutions are not necessarily of the most general type, for to meet the conditions that restrict their choice, μ and ε are taken to be independent of the coordinate to which the transverse component of E (in TE) or H (in TM) is parallel.

Hypersonic Research Facilities at the Ames Aeronautical Laboratory
View Description Hide DescriptionTwo wind tunnels recently completed at the Ames Laboratory of the NACA—the 10‐ by 14‐in. supersonic wind tunnel and the supersonic free‐flight wind tunnel—are capable of providing test Mach numbers well in excess of 5. Since at this time such facilities are relatively uncommon, this paper is primarily devoted to a description of these wind tunnels and their associated equipment.
The treatment of the 10‐ by 14‐in. supersonic wind tunnel is concerned for the most part with the design and operation of the nozzle and diffuser which provides Mach numbers of 3.5 to about 8. Some mention is also made of the pressure measuring and flow visualization equipment. In the case of the supersonic freeflight wind tunnel high test Mach numbers are obtained by firing models at high speed into an oncoming supersonic air stream. Consequently the main emphasis is placed upon the launching techniques, the available range of test conditions, and the methods of obtaining data.

The Application of Rate‐Process Theory to Glass. I. Breaking Strength
View Description Hide DescriptionAn equation relating the ultimate strength of glass and porcelain to time under load is derived using the rate‐process theory of Eyring. The data of Preston and co‐workers are used to calculate the constants in the equation. The agreement between theoretical and experimental results is excellent.

The Application of Rate‐Process Theory to Glass. II. Viscosity
View Description Hide DescriptionIn previous efforts to derive an equation for the temperature‐viscosity relation of glass it has been assumed, tacitly or otherwise, that glass is a simple liquid. Since glass is not a simple liquid, it is necessary to find a model that will, in its reaction to applied stresses, have the same characteristics as a specimen of glass. By the use of Eyring's rate‐process theory, such a model is proposed and several equations relating viscosity to time and to temperature are derived. The equations include an equation that relates the viscosity of any glass specimen to time, one which defines the rate of removal of internal strain, and an equation which relates the viscosity of a specimen an infinite time after beginning of a test to the temperature of the test. This final viscosity is the viscosity usually reported in the literature. It is found that the parameters in the equation reduced to infinite time can be calculated from the chemical composition of the glass and the viscosity of any given glass can be predicted at any temperature over a very wide range. Curves and tables are included to show the agreement of experiment and theoretical values.

Circuit Analysis of Linear Varying‐Parameter Networks
View Description Hide DescriptionThis paper describes a theory of linear varying‐parameter networks which is essentially a generalization of the familiar frequency domain theory of fixed linear networks. Such basic concepts as impedance, admittance, gain, etc., are extended to linear varying‐parameter networks and their important properties are outlined. Extensions are given also of the general mesh and node equations, Thevenin's theorem, dualization, and some other relations that hold in the case of fixed networks. On the whole it is shown that many theorems, properties, and relations that hold in the case of fixed networks may be extended with proper modifications to linear varying‐parameter networks.

Convection Currents in Porous Media. III. Extended Theory of the Critical Gradient
View Description Hide DescriptionThe theory of the critical gradient for onset of thermal convection in a fluid entrapped in a porous medium is extended to allow for the exponential dependence of viscosity upon temperature and for non‐linear vertical temperature‐distributions which characterize transients in heat flow. Although there are approximations in the mathematical treatment, the extended theory agrees rather well with experimental data, as the simple theory does not in certain instances. New experimental data are reported for the critical gradient, obtained largely with silicone fluids in unconsolidated sands.

Theory of Axially Slitted Circular and Elliptic Cylinder Antennas
View Description Hide DescriptionA method proposed by Sommerfeld for solving boundary value problems involving discontinous surfaces has been applied to the general case of a plane electromagnetic wave of arbitrary direction of incidence and polarization diffracting about one or more sections of perfecting conducting circular and elliptic cylinders of infinite length. The solution is in series form, where the series coefficients are independent for the special case of slots of infinitesimal width (slits). Radiation from the slitted cylinder is restricted to discrete right circular cones about the cylinder axis, each cone corresponding to an ordinary wave‐guide mode in the cylinder, while slots of finite width radiate over a continuous range of conical angles. For slots of small but finite width, the relative pattern in the cone α=α_{0} about a circular cylinder of radius a is the same as in a plane normal to the axis of a cylinder of radius a sinα_{0}; patterns of the slotted elliptic cylinder are similarly related, where the analog of radius is distance between foci. Conical patterns are shown for the principal TE and TM waveguide modes in circular cylinders containing one and two diametrically opposed axial slits.

Frequency Factor and Activation Energy for the Volume Diffusion of Metals
View Description Hide DescriptionThe theoretical equations proposed for calculating D _{0} of the diffusion‐constant‐temperature relation are critically discussed in the light of presently available data. It is concluded that none of the relations gives satisfactory agreement with experiment.
Empirical analysis of experimental data covering a wide range of D _{0} and E values showed that the quantity E/T_{m} , where T_{m} is the melting point in °K, is the main factor in determining the value of D _{0}, and that D _{0} depends approximately exponentially on E/T_{m} . In addition to many other diffusion constants, it is shown that the anisotropicdiffusion of zinc and the widely differing diffusion constants for self‐diffusion in α‐ and γ‐iron are included in the proposed empirical correlation.
A possible theoretical basis for the empirical correlation is described based on the idea of local melting or disordering. The quantity E/T_{m} is identified with the entropy of activation.

Thorium Sulfide as a Thermionic Emitter
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On the Fredrickson‐Eyring Theory of the Mechanical Behavior of Metals
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