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Volume 23, Issue 4, 01 April 1952

Statistical Errors in Measurements on Random Time Functions
View Description Hide DescriptionThe statistical errors in time‐average measurements of various properties of (stationary) random time functions are analyzed for their dependence on the averaging interval, the method of averaging, and the statistics of the particular time function under observation. The specific averaging processes considered here are as follows:(1) The continuous time average ,(2) The summation (by discrete sampling techniques) , and(3) The smoothing accomplished by various low‐pass filters (for example, a dc meter).
Here Z(t) may represent the output of a linear or nonlinear device. As a particular example, the measurement of the power in a random noise voltage of band width ω_{ F } is analyzed in detail. The expected root‐mean‐square error approaches asymptotically the value (K/ω _{F} T)^{½}, where K is some numerical constant, depending on the device in question. For (1) and (2) T is the total observation time while for (3) it is proportional to a relevant time constant of the low‐pass filter. A short discussion of the relative merits of correlators and spectrum analyzers is included, together with a brief treatment of the distribution function of the error in the measurement.

The Elastic Constants of Nickel
View Description Hide DescriptionThe elastic constants of nickel have been determined by the pulsed ultrasonic method. Wavevelocity measurements on four nickelsingle crystals of general orientation which were magnetically saturated were combined by the approximation method leading to values of the elastic constants C_{11}=2.53, C_{12}=1.52, C_{44}=1.24, all in units of 10^{12} dyne cm^{−2}.

Effect of Thermal‐Velocity Spread on the Noise Figure in Traveling‐Wave Tubes
View Description Hide DescriptionEffects of thermal‐velocity spread on the noise figure of a traveling‐wave tube have been computed by extending a method of Hahn. To accomplish this, it has been necessary to work out a new theory for the diode‐drift tube and traveling‐wave tube that includes the effect of the thermal‐velocity spread at very high frequencies. Some computations are given for conditions met in practice.

Multiple Scattering of Radiation by an Arbitrary Planar Configuration of Parallel Cylinders and by Two Parallel Cylinders
View Description Hide DescriptionThe formal solution for the scattering of a plane wave by an arbitrary configuration of parallel cylinders previously presented is specialized to consider the case where all the axes lie in the same plane. The scattered wave is expressed as an infinite sum of orders of scattering, the first order being the usual single scattering approximation. It is shown that the far field form of the multiply scattered orders is symmetrical with respect to the plane of the configuration for minimum spacing large compared to wavelength. Hence, for the analogous configuration of bosses on a perfectly conducting plane, departures from the predictions of single scattering theory should occur primarily for the component polarized perpendicular to the elements. The problem of two cylinders is considered in detail, the multiply scattered orders being summed explicitly subject to the above conditions. Approximate solutions for radii very small compared to wavelength are derived, the wavelengths for which the effects of multiple scattering are greatest are investigated, and a criterion for the use of the single scattering hypothesis presented. Solutions for two bosses and a single cylinder parallel to a nonabsorbing plane are also stated. Both the electromagnetic and acoustic cases are treated.

Focusing in a Beta‐Ray Spectrometer with Tilted Sources
View Description Hide DescriptionFormulas are given which express the theoretical line shape obtained in a semicircular beta‐ray spectrometer. The sources are taken to be plane, uniform, and isotropic. Line shapes of a monoenergetic electron group are studied as a function of the angle between source and focal planes. The treatment given applies only to the electrons emerging perpendicular to the magnetic field. However, conditions simulating the requirements for qualitative applicability of the formulas may be obtained practically by slitting out electrons having appreciable momentum components along the field. Two figures are given which illustrate line shapes for various spectrometer geometries.

Studies in Newtonian Flow. IV. Viscosity vs Molecular Weight in Liquids; Viscosity vs Concentration in Polymer Solutions
View Description Hide DescriptionThis is the final installment in the current series entitled ``Studies in Newtonian Flow.'' In this paper, the molecular weight—free‐space function applicable to n‐paraffins m=100 through m=240 at various temperatures is further generalized to apply to homologous series of all Newtonian liquids at constant temperature. The resulting molecular weight function thereby loses some fidelity, and the slopes and intercepts no longer have physical significance. The generalized logarithmic decrement equation nevertheless reproduces viscosity data over extended ranges of molecular weight (at constant temperature) far better than expressions previously proposed. The equation is extended to apply to mixtures of liquids and finally to polymer solutions.

Metallurgical Applications of X‐Ray Fluorescent Analysis
View Description Hide DescriptionTechniques are described for fluorescent analysis using an x‐ray Geiger countergoniometer. Consideration is given to the influence of potential variations, specimen preparation, and thickness of the diffracting crystal.
The observed intensity of fluorescent radiation from a number of common commercially pure metallic elements was compared under a constant primary radiation that can be closely maintained in practice.
Intensities of fluorescent spectra were measured on constituents of Fe‐Ni, Fe‐Cr, and Fe‐Ni‐Cr alloys. Calibration curves correlating line intensity with weight percentage are included for binary Fe‐Ni and Fe‐Cr alloys.
The thickness beyond which the fluorescent intensity becomes constant has been determined for pure iron,nickel, and chromium. Up to the above thickness for each element an empirical plot of fluorescent intensity against thickness of layer has been established. These empirical plots can be applied to measure the thickness of very thin coatings.
Illustrations are given indicating the applications of the fluorescent analytical technique to the study of oxidation and diffusion processes in metallic systems.
An aluminum holder is used for analyzing small quantities of powder derived from chemical or electrolytic extraction of certain phases from alloys. Fluorescent analysis on the extracted phase supplements the diffraction data when a wide solid solubility exists.

Deformation and Fracturing of Thick‐Walled Steel Cylinders under Explosive Attack
View Description Hide DescriptionTests have been conducted on annealed heavy‐walled cylinders of low carbon (1020) steel internally loaded by explosive charges. The purpose of these tests was to obtain basic information on the manner and type of fracturing and plastic flow obtained by extremely high pressures acting for short durations. It was observed that all of the cylinders tended to fracture in long fragments in the same basic pattern, but with variations because of wall thickness and manner of loading. Experimental results indicate that the radial cleavage type of fracture is initiated within the cylinder wall and propagated to the surface, while the shear type fracture associated with the inner portion of the cylinder wall appears as an independent energy relieving process.
Microstructure analysis of the cylinder fragments shows a definite relationship between the type of fracture and the amount of distortion of the grain boundary. Considerable shock twinning is present in the cylinder fragments, and the grain structure near the inner surface shows severe distortion and flow. Strain measurements indicate that considerable plastic strain occurs during the explosive loading and cleavage fractures were always observed to occur in association with considerable plastic deformation.

Influence of Cold‐Work on the Hall Effect of a Metal
View Description Hide DescriptionCold‐work in copper to the extent of 75 percent reduction in the cross‐sectional area resulted in an increase in the Hall constant of 0.01±0.002 times the Hall constant for annealedcopper. The value obtained for the Hall constant for annealedcopper was minus 5.33×10^{−13} volt‐cm/ampere‐gauss.

Structure of Oxide Replicas for Electron Microscopy
View Description Hide DescriptionThe structure of oxide films, which could be used as replicas for electron microscopy, was investigated here. In order to obtain a replica of the metal surface using the oxide film formed on it and isolated from it, the oxide crystals composing the film must be oriented relative to the orientation of the substrate face. The oxide crystals formed on metal, whose atom distances coincided with those of the substrate crystal, could compose a replicating film of the specimen surface. This oxide film did not curl nor expand upon removal from the substrate.

Flow over Thick Plate with Circular Hole
View Description Hide DescriptionFormulas are derived for the scalar potential of a uniform magnetic field parallel to the plane face of an infinite nonpermeable medium in which a circular hole of radius, a, is drilled normally. Outside the hole the formula is an oblate spheroidal harmonic series for which eleven coefficients are given, and inside it is a Bessel function series for which twenty coefficients are given. The case of a flat‐bottomed hole whose depth is greater than its diameter is included. All series converge slowly in the plane of the opening but rapidly elsewhere. When a plane electromagnetic wave falls on such a hole, the fraction of the energy scattered is approximately 11.7(2a/λ)^{4} cosθ if the wavelength λ is much greater than 2a and θ is the angle of incidence. Such a hole in the thick plane wall of a resonant cavity, at a point where H is uniform and E is zero, decreases the resonance frequency ω by 0.2366μa ^{3} H ^{2} W_{m} ^{−1}ω where W_{m} is the magnetic energy in the cavity when H is measured. A lug of radius a affixed to the plane face of a cylindrical rod of the same material, length l and cross section A changes the resistance in the ratio [1+0.3154a ^{3}/(Al)]^{−1}.

Interferometric Analysis of Airflow about Projectiles in Free Flight
View Description Hide DescriptionA description is given of the adaptation to the ENIAC of the interferogram reduction problem for axisymmetric flows. Isopycnal charts from interferograms of projectiles in free flight are presented, and comparison is made with similar studies by other workers using fixed models in a wind tunnel or a circular jet. In general, good agreement is found between density fields obtained by the two methods. Sources of error are discussed; and in particular, it is found that random errors accumulate to effect adversely the density values near the axis of the flow.

Elastic Constants of Beta‐Brass Single Crystals
View Description Hide DescriptionMeasurements of Young's modulus and the rigidity modulus for a set of beta‐brass single crystals of 55 atomic percent copper and for single crystals of beta‐brass near the zinc‐rich phase boundary reveal a dependence of the elastic constants upon composition. Comparison is made with previous results, whereby it is found that the moduli of beta‐brass for different compositions may be obtained by the use of a linear interpolation in terms of the atomic ratio of copper to zinc. Derived quantities are generally related in this manner also. The value of Σ_{111}(Poisson's ratio) is shown to be a positive quantity, in contrast to that derivable from previous results.
Results of bending‐torsion measurements are presented. The agreement between measured values and those calculated from the principal elastic constants provides assurance for the consistency of the measurements.

Temperature Dependence of Young's Modulus and Internal Friction of Single Crystals of Beta‐Brass
View Description Hide DescriptionThe temperature variation of Young's modulus of beta‐brass single crystals of 55 atomic percent copper has been determined. Comparison is made with previously reported results.
Internal friction has been measured at 21 and 42 kilocycles per second at room temperature and as a function of temperature to slightly above the complete disappearance of order. The room temperature decrement is for all crystals of the order of 10^{−4} and mainly independent of amplitude of oscillation. The decrement as a function of temperature shows a ``relaxation peak.'' Zener's theory for alpha‐brass is found to apply and the source of the relaxation is preferential orientation of pair axes of solute atoms in adjacent cells. The heat of activation is about 20×10^{3} calories per mole. The relaxation peak is shown to be characteristic of the disordered state. There seems to be no relaxation phenomenon present in the ordered state.
The effect of precipitation of the alpha‐phase on Young's modulus and the internal friction has been found negligible unless a large amount of precipitation occurs.

Radiation Field of a Square, Helical Beam Antenna
View Description Hide DescriptionRigorous formulas have been derived for the field from a square, helical antenna with a uniformly progressing current wave of constant amplitude. These formulas that have the advantage of great simplicity are of direct use for helical antennas in the meter band, where for practical reasons only square helices are used. Further, in connection with corresponding rigorous formulas for the field from a circular, helical antenna with a uniformly progressing current wave of constant amplitude the present formulas may be used for an investigation of the magnitude of the error introduced in Kraus' approximate calculation of the field from a circular, helical antenna by replacing this antenna with an ``equivalent'' square helix. This investigation is carried out by means of a numerical example. The investigation shows that Kraus' approximate method of calculation yields results in fair agreement with the results obtained from the rigorous formulas. A statement to the contrary made recently in the literature is shown to rest on a trivial error.

A Steady‐State Heat Flow Problem for a Quarter Infinite Solid
View Description Hide DescriptionThe steady‐state temperature field T(x, y) in a homogeneous solid x≥0, y≥0, z arbitrary is studied when the flow out the face y=0 is a prescribed function g(x). Along the face x=0 either the condition T=0 or k(∂T/∂x) = hT is assumed. Of especial interest is the temperature at the face y=0 and the flow at the face x=0; particular attention is paid to the case g(x)=0 for x>a>0. The results have application to situations in which heat is being drawn off at the corner of a solid.

Oxygen‐Free Single Crystals of Lead Telluride, Selenide, and Sulfide
View Description Hide DescriptionAnomalies in the type of conductivity of artificially prepared crystals of lead selenide and lead telluride have been found to be the result of the presence of oxygen. A method has been developed for eliminating oxygen from the specimens by melting the elements into the crucible in an atmosphere of hydrogen. It has also been found possible to grow single crystals of lead sulfide when oxygen is eliminated from the specimen in this way.

The Separation of Cold‐Work Distortion and Particle Size Broadening in X‐Ray Patterns
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Current‐Carrying Wire Loops in a Simple Inhomogeneous Region
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A Study of Oxide‐Coated Cathode by X‐Ray Diffraction Method
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