Volume 22, Issue 2, 01 February 1951
Index of content:
22(1951); http://dx.doi.org/10.1063/1.1699911View Description Hide Description
The propagation characteristics for circularly symmetric TM modes in a coaxial structure with two dielectrics offer many points of interest. For a given mode, the pertinent parameters are the ratio of the dielectric constants of the two media involved, the ratio of the two radii, and the operating frequency, expressed, say, in terms of the cut‐off frequency for the empty guide. Among the results of special interest are the facts, previously pointed out by Frankel and by Bruck and Wicher, that the phase velocity for a given propagating mode may lie between the phase velocities corresponding to each of the two unbounded dielectrics and that, by proper choice of parameters, it is always possible to obtain a phase velocity of a preassigned value higher, of course, than the lower of the two velocities for the unbounded media. This suggests the possibility of using such structures in linear accelerators. The results of an extensive computational program are presented in the form of families of curves showing the dependence of the propagation constant and of the phase velocity on the parameters of interest. Some discussion of the power flow and field distribution is also given.
22(1951); http://dx.doi.org/10.1063/1.1699912View Description Hide Description
The two‐dimensional supersonic irrotational flow of a gas in a jet is studied by use of the Kármán‐Tsien pressure‐volume law. There are two limitations to such a study: (1) since the fluid flow is not continued from the subsonic range, arbitrary boundary conditions must be prescribed; (2) use of the Kármán‐Tsien pressure‐volume relation implies a restriction on the permissible range of pressure, density, and velocity. On the other hand, use of the Kármán‐Tsien law furnishes several advantages: (1) the velocity potential and stream function satisfy the wave equation in the hodograph plane and hence these functions can be easily determined; (2) the mappings between the physical and hodograph planes may be completely characterized and studied in detail. This gain in information should be valuable in the qualitative understanding of phenomena as well as in obtaining first approximations to quantitative solutions. In the case of jets, with free stream lines as boundaries, it is shown that two functions possessing certain desired properties completely determine the Kármán‐Tsien flow. Further, the phenomenon of the periodic recurrence of the free stream jet boundary is explained by a folding property of the map of the flow in the hodograph plane.
22(1951); http://dx.doi.org/10.1063/1.1699913View Description Hide Description
A method is given for determining the residual stress in a sheet material by removing successive uniform layers of material from the surface of a test specimen and measuring the resulting curvature. From the condition of equilibrium of a free specimen, a stress vs curvature relation is derived which holds over the depth to which material has been removed. The method applies when the stress is constant in the plane of the specimen and varies through the thickness. An experimental technique is described which is believed to satisfy the essential requirement that the removal of surface layers should not affect the stress in the remaining material, and a practical example is given.
22(1951); http://dx.doi.org/10.1063/1.1699914View Description Hide Description
An objective has been designed which is particularly suitable for the study of tissue sections. It consists of a large opening polepiece system operated at a focal length of 12 mm. It includes a diaphragm which can be centered (not during operation) and translated on the axis. Angular apertures of as low as 2×10−3 radian with large areas of bright field can be achieved. A simple method of aligning the aperture is described.
22(1951); http://dx.doi.org/10.1063/1.1699915View Description Hide Description
The time dependence of current passed by commercial pentodes has been studied under pulsed conditions of operation. A decay of current is observed in the microsecond time range for those tubes operated for long periods under cut‐off conditions. This decay has been interpreted in terms of the resistance and capacitance of the interface layer known to exist from x‐ray diffraction studies. Techniques are developed and applied to the measurement of this interface resistance and capacitance as a function of temperature. Following the initial current decay, a partial recovery is observed when long pulses are used. This effect results from Joule heating of the interface layer.
22(1951); http://dx.doi.org/10.1063/1.1699916View Description Hide Description
Measurements have been made of the pressure ratio, R, due to thermal transpiration in hydrogen, helium, argon, and nitrogen between a warm temperature of 297°K and cold temperatures of 77.3 or 195°K. It is found that R depends on X, the product of the pressure and tube diameter according to the empirical relation, , where A and B are constants which depend on the gas and on the warm and cold temperatures, and Rm =(T 1/T 2)½. The R against P 2, and threfore X, curves for different gases are found to be related by a ``pressure shifting factor'' f.
The use of these results to correct measurements of adsorption equilibrium and vapor pressures at low pressures and low temperatures is discussed.
Vapor pressures at 77.3°±0.5°K corrected for the thermomolecular pressure effect have been measured for krypton and xenon:
22(1951); http://dx.doi.org/10.1063/1.1699917View Description Hide Description
Experimental and theoretical directional patterns are compared for three polystyrene rod antennas of length variable from about 4 to 10 wavelengths, retaining relative shape in the length direction. The comparison shows that the apparent index of refraction,n, decreases with increasing length. Accordingly, the directional patterns are less sharp than might be expected from the estimated values of n which are constant for a constant relative shape.
22(1951); http://dx.doi.org/10.1063/1.1699918View Description Hide Description
Asymptotic methods are used to find approximate solutions of the acoustic waveequation in a medium in which the velocity is a continuously variable function of one coordinate. It is shown that, when the velocity function has a minimum, undamped normal mode solutions exist and are closely analogous to the internally reflected waves in the case of a medium made up of discrete layers. By converting the sum of the high order normal modes into an equivalent integral, it is shown that superposition of these modes leads to geometrical ray theory modified by diffraction in a manner that may be computed from the incomplete fresnel and airy integrals.
22(1951); http://dx.doi.org/10.1063/1.1699919View Description Hide Description
In dealing with numerical values for relative intensities derived from the Debye‐Scherrer technique, the alteration of diffracted intensities produced by absorption in the sample cannot be ignored. Claassen has shown how this effect can be allowed for in the case of homogeneous cylindrical samples. This paper deals with a sample consisting of a cylinder surrounded by another annular cylinder both when the core is inert (i.e., absorbing and producing only extraneous scattering) and when the annulus is inert. The method is applied to show how the diffraction pattern for a liquid enclosed in a glass container may be corrected for the diffuse diffraction of the container as well as for absorption in the liquid and in the glass.
22(1951); http://dx.doi.org/10.1063/1.1699920View Description Hide Description
Coefficients of static friction of six metals (Fe, Ni,Cu,Pb, Sn, and Zn) have been measured at temperatures ranging from liquid helium up to room conditions (and in two cases above this). Shear strengths and hardnesses of these metals were measured over the same range of temperatures. It was found that in spite of the generally large variation of both of these latter quantities with temperature, their ratio is in most cases dependent, to only a slight extent, on temperature, following rather closely the change of the static‐friction coefficient with temperature. This fact tends to substantiate the adhesion theory of friction proposed by F. P. Bowden.
22(1951); http://dx.doi.org/10.1063/1.1699921View Description Hide Description
A vector analytic treatment is given of the formation of undisturbed fringes by an ideal Mach‐Zehnder interferometer with an extended source. The path difference of two interfering rays at an arbitrary point in the field is found to depend, in a simple way, upon the source point from which the rays originate, the field point examined, and a dyadic which is a function of the unit normals to the last mirror and divider plate of the interferometer. The fringe clarity condition, that all pairs of interfering rays reaching the field point have path differences within a specified range, is developed in the form of an inequality. Analysis of this fundamental inequality shows that all admissible area sources must be areas enclosed between two conics in the source plane. For fringes perpendicular to the plane of centers of the interferometer elements, the optimum source is a circle with radius inversely proportional to the square root of the number of clear fringes desired. This result holds for all interferometers of parallelogram planform. For fringes parallel to the plane of centers, each interferometer orientation presents a special case. The optimum source area is obtained for two of these, viz., the 45° and 30° interferometers.
Periodic Statistical Distortion of Unidirectionally Ordered Diffractors, with Application to Collagen22(1951); http://dx.doi.org/10.1063/1.1699922View Description Hide Description
The diffraction expected of distorted, one‐dimensionally ordered cylinders (fibrils) is considered quantitatively. The distortion involved is statistically of cylindrical symmetry about any point in the fibril, and periodic along the fibril axis. An important case is that of the ``mixed perfect and imperfect fibril,'' in which, at some axial levels, distortion is absent, and at others it is appreciable. For such systems it is shown that the reciprocal‐space disk corresponding to a given diffraction layer line may be regarded as composed of three sub‐disks: one of perfection, whose central intensity is maximal and whose diameter is small and independent of layer‐line index; another of longitudinal or axial imperfection, whose central intensity is also maximal; and a third, related to radial imperfection, whose intensity is noncentrally maximal. Both types of imperfection sub‐disk expand linearly in diameter with increase in index.
It is demonstrated briefly that certain dry collagen specimens exhibit small‐angle diffraction in which the characteristics of the three types of sub‐disk are apparent.
22(1951); http://dx.doi.org/10.1063/1.1699923View Description Hide Description
Approximate formulas are derived for computing the effect of mechanical resistance on the electrical characteristics of a piezoelectric crystal system for the case of a general reactive termination and low loss. A comparison of values computed on the basis of these formulas and exact calculations is presented.
22(1951); http://dx.doi.org/10.1063/1.1699924View Description Hide Description
The density in supersonic flow was measured by the absorption of soft x‐rays. The equipment is briefly described. Data obtained in undisturbed flow at M=2.83 are compared with values computed from Pitot pressure measurements. Measurements of the density distribution across a shock wave on a wedge‐shaped model are presented. The suitability of the method, its limitations, and improvements of the technique are briefly discussed.
22(1951); http://dx.doi.org/10.1063/1.1699925View Description Hide Description
Improved instrumentation of the radar system has permitted a more accurate analysis of range‐time records of meteor echoes and enabled the meteor deceleration to be determined in a few special cases. Three illustrative examples are described in which the measured mean decelerations were −0.48, −1.1, and −1.5 km sec−2. Velocity data from a continuous wave Doppler system were also available for these meteors and are compared with the radar data.
Using existing atmospheric density values and Lovell's scattering formula, it is computed that the ionizing efficiency, or the fraction of the kinetic energy of the meteor converted to ionization, is 10−6 for a 60‐km/sec meteor and 10−8 for a 20‐km/sec meteor. If lower values of the air density are adopted, the efficiency figures are increased and at the same time the gap is narrowed between the rates of electron production deduced from loss of mass considerations and the rates calculated from the radar data. More statistical data on radar meteors and further information on the ionizing properties of 1000 electron‐volt atoms are required before definite conclusions can be drawn.
22(1951); http://dx.doi.org/10.1063/1.1699926View Description Hide Description
A high resolution camera was constructed for small angle x‐ray scattering. Measurements with this camera on Dow latex 580G exhibit a number of concentric rings. Each ring is associated with a theoretical maximum of scattered intensity predicted by the spherical x‐ray form factor corrected for packing.
The particle diameter is then computed from the position of each ring. Twenty measurements yield a diameter of 2780A with a probable error of less than ±1 percent.
22(1951); http://dx.doi.org/10.1063/1.1699927View Description Hide Description
A theoretical treatment is given for the operating characteristics of molecular drag type pumps. The present work is based on kinetic theory and is limited to high vacuum operation. The solutions are simple and may be applied readily to practical pump designs. They lead to performance characteristics which are thought to be accurate to ±10 percent.
22(1951); http://dx.doi.org/10.1063/1.1699928View Description Hide Description
Tests designed to produce supersonic streams at ten and sixteen times the local speed of sound are described. In contrast to the usual wind tunnel apparatus, a conical nozzle is used for the expansion section, and the supply pressure is varied throughout a wide range. Some properties of the flow at high Mach numbers are discussed, and, in particular, data are given showing a systematic dependence of Mach number on stagnation pressures, a phenomenon not previously reported.
22(1951); http://dx.doi.org/10.1063/1.1699929View Description Hide Description
The basic theory of calculation of the capacitance of a given geometrical configuration by the use of subareas is advanced and applied to solve the long‐standing problem of the accurate evaluation of the capacitanceC of a cube of side a. The best previously published determination is 0.62211a<C<0.71055a. The value obtained of C≈0.655a esu is both a lower limit and very close to the exact value.
22(1951); http://dx.doi.org/10.1063/1.1699930View Description Hide Description
Gold blacks, prepared by evaporating gold from a tungsten filament in tank nitrogen at several mm pressure, were found to contain tungsten oxides which greatly affected the optical and electrical properties.Deposits containing more than 0.5 mole percent of tungsten oxides were black and showed resistivities 103 to 108 times that of bulk gold. The resistivities of gold blacks increased on exposure to oxygen. On the other hand, oxide‐free deposits were yellow and possessed a low stable resistivity, unaffected by exposure to oxygen. Exposure to air or oxygen caused an increase in the electrical resistance, and optical transmission of films of tungsten dioxide and tungsten trioxide evaporated in high vacuum. It was concluded that evaporated films of pure gold are unaffected by exposure to air and that the changes in optical and electrical characteristics, often observed in evaporated goldfilms exposed to air, may be attributed to contamination by oxides of tungsten. It was also concluded that so‐called gold blacks are black because of the presence of tungsten oxides, since gold evaporated in pressures of several millimeters of oxygen‐free nitrogen formed bright reflecting films rather than black absorbing deposits.