Volume 24, Issue 9, 01 September 1953
Index of content:
24(1953); http://dx.doi.org/10.1063/1.1721452View Description Hide Description
Electron microscopic evidence is presented in support of the hypothesis that black carbon resulting from pyrolysis of gaseous hydrocarbons is produced through the intermediate formation of droplets of complex hydrocarbons. Electron diffraction studies further confirm this hypothesis if, as has been found for particles of carbon blacks, the droplets consist in part of graphitic nuclei arranged with their basal planes tangential to the dropletsurface. The carbonization of small solid spherules of highly cross‐linked organic polymers is described, and it is shown that the morphology of the carbonization products is wholly analogous to those for pyrolytic carbon and carbon blacks. It is suggested, therefore, that the formation of carbon by the carbonization of solids and by deposition from the gas phase occurs through similar mechanisms and that the two processes are simply two extremes in an infinite series of processes which are all fundamentally alike.
24(1953); http://dx.doi.org/10.1063/1.1721453View Description Hide Description
The presence of stiffness in a stretched string vibrating between fixed supports raises all the natural frequencies over those for a perfectly flexible string. The presence of nonuniformity in cross‐sectional area along the string changes some or all of the frequencies from those for a perfectly uniform string, the amount and direction of change depending on the form of the nonuniformity. These changes in frequency may introduce error into the calculation of the average cross‐sectional area of a fiber by means of the vibroscopic technique, wherein the mechanical resonance of a stretched fiber is observed under oscillating mechanical or electrostatic forces. In this paper the natural frequencies are calculated with both the stiffness and the nonuniformity taken into account to first‐order terms. The relation between the average cross‐sectional area and the natural frequencies is analyzed. Consideration is given to the manner in which the changes in frequency and shifts of the nodes, due to nonuniformity, determine the detailed form of the area variation. The characterization of nonuniformities in terms of certain arbitrary parameters is shown to lead to the possibility of calculating the average area by measuring the natural frequencies in only the first and second modes and of calculating the maximum or minimum area by measuring also the nodal shift in the second mode.
The Identification of Individual Hygroscopic Particles in the Atmosphere by a Phase‐Transition Method24(1953); http://dx.doi.org/10.1063/1.1721454View Description Hide Description
It is shown that in many cases the measurement of the relative humidity at which a hygroscopic particle becomes liquid can be used to establish the chemical composition of the particle. An apparatus is described which produces a stream of air of constant temperature and variable humidity. Using this apparatus the phase‐transition point was determined for particles collected on spider webs. These particles were sampled in the Sydney area on the ground and from an aircraft, and it is shown that the measured values of relative humidity for the solid‐liquid phase transition agreed with the hypothesis that the hygroscopic particles were composed of sea salt. Direct microscopic observation was used to follow the behavior of the particles; the technique was capable of dealing with particles down to 10−12g.
24(1953); http://dx.doi.org/10.1063/1.1721455View Description Hide Description
The summation of series involving the roots of certain transcendental equations having real roots is achieved by elementary considerations. The method is illustrated by several examples representative of those which may arise in applications. In addition to summing series, the method can be used to obtain the least positive root of the transcendental equation to any desired accuracy with but little computation.
24(1953); http://dx.doi.org/10.1063/1.1721456View Description Hide Description
It was shown earlier that plastic grating‐replicas mounted upon eighth‐inch specimen screens were practical internal standards and that they could be accurately calibrated independently by spectroscopic means. Metallic replicas of diffraction gratings have been made by a direct‐stripped method. These can still be direct‐stripped easily and without damage to the original grating, and the optical quality of these pre‐shadowed all‐metal replicas is better than that of the plastic replicas. Because of their superior optical properties, the spacing can be determined spectroscopically more conveniently and with greater accuracy. In addition, the metal‐gratings are more stable than the plastic ones. The electron microscopy of the metallic replicas and the accuracy and constancy of their magnification measurement is discussed.
24(1953); http://dx.doi.org/10.1063/1.1721457View Description Hide Description
A process is described in which radioactive radiation traverses a soliddielectric medium to charge a collector electrode. This process offers a simple method of studying effects of radiation on matter such as bombardment‐induced conductivity, secondary emission, charge soakage, and radiation absorption. Typical data are given. Possible application of this process for the construction of a current or voltage source for use in electronic devices is discussed.
24(1953); http://dx.doi.org/10.1063/1.1721458View Description Hide Description
The paper is concerned in the main with a Maxwellmaterial, which corresponds to a model having a spring and dashpot in series. The equation for longitudinal wave propagation in rods is shown to be equivalent to the telegraph equation, and solutions of transient wave problems are treated briefly in the Appendix using the Laplace transform technique. Impact on a semi‐infinite rod is considered in detail in the report. A method of superposition of images is discussed to use this solution to solve boundary value problems for finite rods. The resulting stress distributions are discussed and contrasted with those for an elastic rod. The natural grouping of problems is discussed according to the relative magnitude of the duration of interest, the relaxation time, and the wave traverse time. The influence of the idealization involved in the Maxwell model is briefly touched upon.
24(1953); http://dx.doi.org/10.1063/1.1721459View Description Hide Description
It has been shown that an approximate solution for the diffraction of an electromagnetic wave by an aperture in a plane conducting screen can be obtained from a single component of the Hertz vector and that the results can be applied to calculating the field of apertures which are sufficiently large as compared to the wavelength of the incident radiation. The solution rests upon an evaluation of an inhomogeneous scalar boundary‐value problem. An infinitesimal wavelength approximation leads to a simple Kirchhoff‐like formula which is found to be identical to that obtained by Neugebauer who derived it from geometrical optics as first approximation. The special case of diffraction by a circular aperture is treated in detail, and experimental measurements by which the theory was checked are cited.
24(1953); http://dx.doi.org/10.1063/1.1721460View Description Hide Description
This paper presents a new method for the measurement of surface stress. By the use of test pieces plated with copper, the stress is measured by observing the flecks on the surface produced by cyclic stress. The variation in the appearance of flecks which is due to the change of load is very sensitive at a proper load, so an accurate determination of the surface stress is feasible.
The stress concentration factor in torsion is obtained experimentally by the method described for circular shafts with a circumferential notch in each. The results are compared with theoretical values, calculated from two different formulas previously derived by the author and Sonntag, respectively. It is confirmed that the experimental results obtained here are in good agreement with those calculated by the author's formula.
Solution of Electromagnetic Scattering Problems as Power Series in the Ratio (Dimension of Scatterer)/Wavelength24(1953); http://dx.doi.org/10.1063/1.1721461View Description Hide Description
It is shown that the scattered field and the field inside the body can be expressed formally as power series in the above ratio, the calculation of successive terms in the series requiring the solution of standard problems in potential theory, together with the evaluation of certain potential integrals, so that the process can be carried as far as desired if Laplace's equation can be solved in the coordinate system appropriate for the body. The convergence of the series for the scattered field becomes progressively worse as we recede from the body, but an alternative expression for the field, also proceeding in powers of the same parameter, gives a representation which is valid everywhere except in the immediate neighborhood of the body (in particular, in the wave zone) and which does not suffer from this defect. The case of a perfect conductor, or diffraction through a hole in a perfectly conducting screen, can be treated as particular cases of the general theory. The paper can be regarded as an extension of Rayleigh's work, which confines itself to the first terms in the series.
24(1953); http://dx.doi.org/10.1063/1.1721462View Description Hide Description
The method previously described of solving electromagnetic scattering problems as power series in k is here applied to the ellipsoid, the first three terms in the series being obtained. The second term in the series for the wave zone field (that proportional to k 3) vanishes, and the same is true of any body possessing a center of symmetry. Thus the terms in k 2, k 4 in the wave zone field are here obtained. The direction and polarization of the incident wave, and the electromagnetic constants of the ellipsoid, are arbitrary. The final results are expressed in terms of certain elliptic integrals which are functions of the three principal axes of the ellipsoid. These integrals can all be expressed simply in terms of just two such integrals; they become elementary integrals in the case of a spheroid. Various special cases are considered, including that of a perfectly conducting elliptical disk and the complementary problem of diffraction through an elliptical hole in a perfectly conducting screen.
24(1953); http://dx.doi.org/10.1063/1.1721463View Description Hide Description
The statistical definition of information is compared with Boltzmann's formula for entropy. The immediate result is that information I corresponds to a negative term in the total entropyS of a system. .A generalized second principle states that S must always increase. If an experiment yields an increase ΔI of the information concerning a physical system, it must be paid for by a larger increase ΔS 0 in the entropy of the system and its surrounding laboratory. The efficiency ε of the experiment is defined as ε = ΔI/ΔS 0≤1. Moreover, there is a lower limit k ln2 (k, Boltzmann's constant) for the ΔS 0 required in an observation. Some specific examples are discussed: length or distance measurements,time measurements, observations under a microscope. In all cases it is found that higher accuracy always means lower efficiency. The information ΔI increases as the logarithm of the accuracy, while ΔS 0 goes up faster than the accuracy itself. Exceptional circumstances arise when extremely small distances (of the order of nuclear dimensions) have to be measured, in which case the efficiency drops to exceedingly low values. This stupendous increase in the cost of observation is a new factor that should probably be included in the quantum theory.
24(1953); http://dx.doi.org/10.1063/1.1721464View Description Hide Description
A duality between the two types of negative resistance is noted. It is demonstrated that with series or parallel ``resonant circuits'' one can form either class by using either a nonlinear choke or nonlinear condenser. This ac characteristic can be converted to a similar dc one by using a bridge rectifier. With such an arrangement one can excite oscillations in a resonant circuit or produce relaxation oscillations. Several quite general oscillatory circuits are described, as are some multistable and counter circuits. The interaction with mechanical systems are considered.
24(1953); http://dx.doi.org/10.1063/1.1721465View Description Hide Description
The method of Kac and Siegert for finding the output probabi ity density characteristic function for receivers with square law envelope detections is discussed, and a parallel development is given for the square law rectifier. Procedures are then outlined for determining the probability density functions directly, i.e., without solving the eigenvalue problem or inverting the characteristic function. The method depends on expanding the density function in an orthonormal series, the coefficients of which are expressed in terms of cumulants, which in turn are obtained from the system kernel by straightforward quadratures.
As an example to illustrate the procedure, a receiver with Gaussian IF and Gaussian audio‐frequency pass characteristics is treated in detail, and the output probability density functions are found for various sinusoidal input signal strengths and IF vs audio band‐width ratios.
24(1953); http://dx.doi.org/10.1063/1.1721466View Description Hide Description
Chips of a gold‐silver alloy were made by orthogonal cutting with apparatus which permitted the determination of the chip geometry and cutting forces. From these data the stresses and strains and the shear and friction energies were calculated. Three rake angles were used to obtain different shear strains. The energy stored in the chips was determined as the difference in the heat effects associated with the dissolution in liquid tin of samples of cold worked and annealed chips in an isothermal calorimeter of high precision. With increasing strain the stored energy increased, but the ratio of the stored energy to the shear energy decreased.
24(1953); http://dx.doi.org/10.1063/1.1721467View Description Hide Description
An optical technique, reported in a previous paper, has been used to measure surface oscillations on a series of thick 5.5‐in. diam steel plates of different thicknesses while they deform under explosive attack. Data obtained from the four 1025 steel specimens illustrated in the previous paper, and data obtained from two additional specimens have been analyzed partially. Results are compared with predictions from the theory of elasticity for the case of a diverging pulse. Elementary theory, known to be incorrect in the physical regime studied, is shown to give many satisfactory predictions for large distances from the charge.
24(1953); http://dx.doi.org/10.1063/1.1721468View Description Hide Description
A noniterative numerical method has been found for solving a partial differential equation when its boundary conditions are not known on the entirety of a closed boundary. Under such conditions, the iterative numerical methods which are generally used, such as the relaxation technique, are not applicable. As an example, this noniterative numerical method has been used to calculate the shapes of a pair of beam forming electrodes for use in an electron gun in which rectilinear flow is desired. The calculated shapes are in almost complete agreement with Pierce's experimental results. Equipotential surfaces calculated by this method have been checked by means of an electrolytic trough which employs a semiautomatic detecting and plotting system.
24(1953); http://dx.doi.org/10.1063/1.1721469View Description Hide Description
The dielectric constant έ/ε0 and loss tangent tanδ of barium‐strontium titanateceramics were measured as a function of temperature and static electric field at frequencies of 10 kc, 500 kc, and 3000 Mc. No frequency dependence of έ/ε0 was apparent at temperatures above the Curie point. An increase in tanδ was observed in going from the low frequencies to 3000 Mc, but above the Curie point the values were not excessively large. A description of the 3000 Mc bridge construction and operation is given.
A More Exact Treatment of the Equations Describing Dielectric Relaxation and Carrier Motion in Semiconductors24(1953); http://dx.doi.org/10.1063/1.1721470View Description Hide Description
Previous treatments of the linearized equations describing hole and electron flow in a homogeneous semiconductor have not been wholly satisfying mathematically. An exact treatment of these equations is undertaken and it is demonstrated that the departure from complete local charge neutrality implicit in the equations corresponds to a polarization attributable to local variations of conductivity. The dielectric relaxation is described and exact expressions for the effective mobility and diffusion coefficients are obtained. The corrections to the older values are of magnitude τ r /τ, where τ r is the relaxation time and τ the lifetime. For semiconductors, these corrections are negligible.