Volume 24, Issue 12, 01 December 1953

Thermal Contraction of a Split Hollow Cylinder
View Description Hide DescriptionConsider a long hollow cylinder which is radially split along its entire length. When such a cylinder is heated, its inner radius undergoes a change δa. The cylinder is called stable if δa≤0. An approximate solution for δa is derived and is used to determine conditions for stability. The pressure against the inner surface required to prevent the contraction δa is also derived.

Exact Interpolation of Band‐Limited Functions
View Description Hide DescriptionA general formula is derived for the spectrum of a multiply‐periodic, amplitude modulated sequence of pulses. The result is used to show that a function which lies in a frequency band (W _{0}, W _{0}+W) is completely determined by its values at a properly chosen set of points of density 2W. This verifies a supposition commonly accepted in communication theory.
The well‐known, exact interpolation formula for a function f(t) in a band (O, W) is .The function is thus determined by its values at a set of evenly spaced points ½W apart.
For a function f(t) in a band (W _{0}, W _{0}+W) it is shown that an exact interpolation formula is in which k is subject to weak restrictions and .Thus, the function is determined by its values at a set of points of density 2W, but the points consist of two similar groups with spacing 1/W, shifted with respect to each other.

Attenuation of Gamma Rays. II. Transmission Values for Various Materials and Geometries
View Description Hide DescriptionA discussion of the effect of variation of the total absorption coefficient on gamma‐ray transmission probabilities is given, which leads to estimates of the build‐up factors for a material of arbitrary atomic number Z.
Estimates are made of the photon and energy densities arising from a plane of sources, a line of sources, and a point source in an infinite homogeneous medium, where the material of the medium is (1) iron and (2) lead.

Microwave Diffraction Measurements in a Parallel‐Plate Region
View Description Hide DescriptionMany infinite two‐dimensional electromagnetic‐scattering problems are strictly equivalent to the configuration obtained from the image principle by placing a finite‐scattering obstacle between two parallel, infinite, and perfectly conducting planes and illuminating it with a plane or cylindrical incident wave confined to the parallel‐plate region.
An experimental approximation to this arrangement is described for use in the 3‐centimeter wavelength region. Finite rectangular parallel metal plates support a transverse incident electromagnetic wave with the electric field oriented perpendicular to the plates. Absorbing wedges at the boundary of the region reduce reflections from this discontinuity. The electromagnetic field scattered from any particular obstacle may be investigated by means of a dipole probe introduced into the region through a moveable section of one of the plates.
The success of this technique is demonstrated by comparing measurements of the total field scattered by infinite conducting wedges of included angle 0, 45, and 90 degrees with the known theoretical expressions, for perpendicular incidence. Agreement with theory is good.
The effect of finite thickness of the diffracting screen (case of 0° wedge) in increasing the amplitude of the scattered wave is noted and compared to theoretical results derived for scattering from a thin conducting half‐plane with a cylinder superimposed on the edge.

Theory of the Formation of Bubbles
View Description Hide DescriptionWe have not yet obtained a perfect theory of bubble formation. In this paper the perfect theory of the formation of bubbles in the case where the bubbles of vapor are nucleated spontaneously in pure liquid is presented. This is done by the systematization of the classical theory of M. Volmer (Kinetik der Phasenbildung, 1939) and the theory of D. Turnbull and J. C. Fisher [J. Chem. Phys. 17, 71 (1949)] and it coincides satisfactorily with the experiment of K. L. Wismer [J. Phys. Chem. 26, 301 (1922)].
Theory must be advanced further so as to afford a perfect explanation of the processes of boiling, cavitation and the critical phenomena of the movement of soil moisture [S. Takagi, Monographs on Theoretical Soil Physics; Theoretical Considerations on the Thermodynamical and KinematicProperties of Soil Moisture (not yet published)]. To effect this object, the author has calculated the rate of formation of bubbles at a surface. The theoretical value, however, of the negative pressure at which the liquid fractures does not coincide by any means with the atmospheric pressure in the process of boiling. This is true also in the process of cavitation and in the process of critical phenomena of the movement of soil moisture. Some other factors must be introduced in order to bring the theory to a state of practical value.

Variational Methods for Problems in Resistance
View Description Hide DescriptionSchwinger's variational methods are applied to a resistance problem with mixed boundary conditions. By the use of two formulations, both upper and lower bounds to the resistance are obtained. Results are given for a cylinder subject to given boundary conditions for a number of values of the relevant parameters.

Approximate Solutions of the Space‐Charge Problem for Some Unusual Electrode Geometries
View Description Hide DescriptionAn approximation technique for computing the space charge limited current between electrodes of unusual and complicated geometry that cannot be treated rigorously is discussed and applied to several electrode systems involving both cylindrical and sphreical emitters. This method was originally suggested by Matricon and Trouvé and by O'Neill. All that is required is a knowledge of the electrostaticcapacitance of the system concerned. Many electrode systems of practical importance which were heretofore not susceptible of calculation are amenable to this technique.

Response of Two‐Material Laminated Cylinder to Simple Harmonic Environment Temperature Change
View Description Hide DescriptionIn current aeronautical research, rapidly‐responding thermocouples and hot‐wire anemometers are required. The use of oxide cylinders coated with more or less thin layers of metal effects substantial improvements in rates of instrument response. The theory and results of numerical calculations for six typical situations are given. It is shown that for ratios of metal thickness to over‐all radius of 0.1, response amplitude gains of the order of 4 or 5 are to be expected as compared with typical gains of the order of 10 or more for infinitesimal shells (surface layers).

Shapes of Floating Liquid Zones between Solid Rods
View Description Hide DescriptionThe present paper seeks to describe the shapes of liquid floating zones between solid rods of silicon and of germanium and to discuss stability conditions. The shapes were deduced from the equation given by Laplace, ,where p indicates the pressure difference across the surface membrane of a liquid at any point, R _{1} and R _{2} are the principal radii of curvature at that point, and γ is the surface tension of the liquid.
The floating liquid zone is analyzed within a wide stability range. Its dimensions were theoretically determined and experimentally confirmed.

Preparation of p — n Junctions by Surface Melting
View Description Hide DescriptionA new method is described for preparation of p — njunctions in single‐crystal semiconductors: the upper part of a slice cut from a single‐crystal semiconductor is melted by radiation. Impurities of the opposite type than those present in the crystal are introduced into the melt. Upon slow solidification of the melt a single crystal is obtained with a p — njunction at the original position of the solid‐liquidinterface. The method is capable of producing multiple junctions.
The influence of (a) heater temperature, (b) forced cooling, and (c) thickness of the slice on the position of the solidliquidinterface is calculated for a one‐dimensional model, assuming that the temperature difference between bottom and top of the semiconductor is small compared to the melting temperature of the semiconductor. The time constant characterizing the rate of reaching equilibrium conditions after a sudden small change in heater temperature is estimated.

The Generation of Wind Waves on a Water Surface
View Description Hide DescriptionThe statistical methods for treating continuous media developed elsewhere are applied to the generation of surfacegravity waves. The wind stress is assumed to be everywhere normal to the disturbed surface of the water and caused by a known ensemble of ``gusts.'' Each gust is considered to be a center of high or low pressure, which moves with the mean wind speed, and has a radius L, and duration T. The rms value of the variable wind pressure is assumed to vary systematically from point to point in a storm. The calculations are made for an idealized, long continuing storm; before applying the statistical equations, the effect of a single gust is calculated.
It is shown that the single gust produces a V‐shaped wake, which, after the gust has blown itself out (t>T) can be considered as a packet of free gravity waves, which moves and spreads under the influence of divergence and dispersion.
The results of the statistical calculation are compared with known general facts, and with an actual storm. From the fact that the storm waves have a non‐sinusoidal character, and arrive at any one point in groups of 5 to 10 crests, it is deduced that the duration of a gust is from 15 to 30 seconds. From the fact that the majority of the wave energy travels in directions that are within 30° of the wind, and with phase velocities that are nearly equal to the wind speed, the mean radius of the gusts is deduced to be about 40 meters in the case of a wind speed of 20 meters per second.
The crest length of the waves is proportional to the distance r from the storm, and inversely to its diameter, D; when r/D=10, the dominant length of the crests is 2.2 wavelengths.
The rms displacement, H, of the sea‐surface from its horizontal mean is a function of the parameters already mentioned and of P, the rms value of the variable component of the wind pressure at the center of the storm; for the idealized storm considered, and for r/D≫1, this is approximated by ,all quantities being in centimeters, including P, which is measured in centimeters on a water barometer. Comparison with data for an actual storm indicates that this theory requires a value of P that is possibly 10 times greater than its actual value.
While the theory explains many of the phenomena of storm waves, it is therefore incapable of accounting quantitatively for the wave height. The possible reasons for this inadequacy are discussed. The relation of the theory to Jeffreys' sheltering theory is also discussed, and it is shown that both postulate that the variable component of the wind stress is normal to the water surface. The sheltering theory also postulates that the wind pressure lags 90° behind the surface disturbance. A similar phase lag is a consequence of the assumptions of the present theory.

The Electron Microscopy of Photographic Grains. Specimen Preparation Techniques and Applications
View Description Hide DescriptionSeveral electron microscopical specimen preparation techniques are described, including two replica techniques. The most important specimens utilize the thin film of the silver‐gelatin complex which exists as a tightly fitting skin around the photographic grains. This relatively inert and insoluble complex is referred to as the combined envelope; a study of this structure is given.
Latent image centers are enlarged in several ways so as to be readily resolvable in the electron microscope. After this partial development the matrix or intergrain gelatin is removed and the grains are fixed. The final specimen consists of developed centers retained by the combined envelope.
Applications of the replica technique to grain shape, size distribution, and growth nature of photolytic silver are given. Utilization of the combined envelope in conjunction with the special development techniques to provide information which substantiates independent sensitometric data is also demonstrated.

Electron Microscopical Studies of the Latent Image Obtained by Exposures to Alpha Particles, X‐Rays, and Light
View Description Hide DescriptionThe latent image of ordinary photographic emulsions has not been resolved. However, the slightly enlarged latent image as obtained by physical gold development can be demonstrated by means of the electron microscope. For the case of a fast negative emulsion it is shown that different types of exposures result in latent image centers of significantly different size distribution characteristics. High‐intensity alpha‐particle and x‐ray exposures produce a very large number of finely dispersed centers; irradiation with light of optimum intensity and 1/100 sec duration forms a small number of centers; only very few specks result from exposures to light of very low intensity. The patterns observed are in line with expectations based on current photographic theory.
 LETTERS TO THE EDITOR


A Modification of R‐PAC for Interpretation of Patterson Maps in X‐Ray Crystal Analysis
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Resistivity of Thin Silver Films
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Experiments in Hydrodynamic Lubrication Using Water as a Lubricant
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Comment on ``The Calibration of Photographic Emulsions for Electron Diffraction Investigations''
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Reply to Comment on ``The Calibration of Photographic Emulsions for Electron Diffraction Investigations''
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Note on the Stress Dependence of the Activation Energy of the Rupture Process
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Effect of Cross‐Section Area and Compression upon the Relaxation in Permeability for Toroidal Samples of Ferrites
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