Volume 23, Issue 10, 01 October 1952
Index of content:
23(1952); http://dx.doi.org/10.1063/1.1701987View Description Hide Description
Schilieren spark snapshots spaced at electronically controlled intervals of several hundredths of a millisecond show the emergence of the shock wave and the formation of the vortex ring at the end of a cylindrical shock tube, open to the atmosphere. The axial positions of the vortex ring and shock front are plotted as a function of time for the first millisecond, in which time the vortex forms and is accelerated to about three‐quarters of the theoretical particle velocity of the mass flow following the initial plane shock. The diameter of the vortex ring increases nonlinearly with time and distance.
23(1952); http://dx.doi.org/10.1063/1.1701988View Description Hide Description
A method of expanding expressions of the type J(ξ)Y(σ)−J(σ)Y(ξ) and J′(ξ)Y(σ)−J′(σ)Y(ξ) is given. Here J and Y are Bessel functions of the first and second kind. These forms occur frequently in physical problems with cylindrical symmetry. The type of expansion used here can be used with other functions that are solutions of second‐order differential equations. The use of these expansions allows the development of theories for two rheometers used for determining dynamic mechanical properties of liquids. In these mathematical treatments, the inertia of the sample is taken into account.
23(1952); http://dx.doi.org/10.1063/1.1701989View Description Hide Description
A generalization of ordinary circuit theory which enables one to define impedances in any periodic structure is developed, based on the concept of expansion of electromagnetic fields in terms of a set of linearly independent basis fields. Techniques for measurement of impedances in a periodic structure are described, involving a determination of the parameters of a coupling system by an extension of the well‐known nodal shift method.
23(1952); http://dx.doi.org/10.1063/1.1701990View Description Hide Description
An approximate evaluation of the branch‐cut integral which occurs in the rigorous solution of the Boltzmann equation for intermediate and large distances is of importance in shielding problems. Such an evaluation leads to Eq. (20) for the point source and Eq. (24) for the plane source. Equation (20) is actually 23 percent high for zero absorption (f=0) and rσ=7, but the error decreases with increasing rσ and f. It is seen that the branch‐cut term is not simply the contribution of noncollided neutrons.
Figure 2 is a plot of the region in the f−rσ plane where the two terms are comparable.
23(1952); http://dx.doi.org/10.1063/1.1701991View Description Hide Description
A small, stainless steel, two‐dimensional source flow nozzle supplied with bottled nitrogen was used for the condensation investigation. It was found that the nitrogen supersaturates approximately 15°K or 1.2 Mach numbers when expanded from stagnation conditions of 70°F and pressures of 8.21 and 16.15 atmos. A numerical method for solving the equations of motion with the aid of the experimental data allows the computation of the fluid temperature during the condensation process. The addition of small amounts of carbon dioxide reduced the degree of supersaturation obtainable with bottled nitrogen.
23(1952); http://dx.doi.org/10.1063/1.1701992View Description Hide Description
The transit time spread due to difference in initial velocity in a planar diode has been calculated for the case of nonhomogeneous velocity distribution. The spread is given as a function of the current for two practical cases, the normal diode and an inverted diode (a beam reflected in a diode space). The spread is also given as a function of anode voltage within certain limits. The method may be used to estimate the influence of transit time spread on transit time devices. A special application is described.
23(1952); http://dx.doi.org/10.1063/1.1701993View Description Hide Description
The formal multiple scattering solution obtained previously for the scattering of a plane wave by an arbitrary configuration of parallel cylinders is applied to the finite grating of cylinders and to the reflection grating of semicylindrical bosses on a perfectly conducting infinite plane. A far field solution in closed form for spacing large compared to wavelength and radius is obtained on neglecting the ``end effects.'' It is found that for the transmission grating both polarizations may be markedly affected by multiple scattering; for the reflection grating, however, the effects are much more pronounced for polarization perpendicular to the elements. The case of radii≪λ is investigated in detail; the λ's for which the effects are greatest are determined, and various intensity curves are presented. The bright and dark bands appearing on these curves (overlaying the usual continuous spectra observed with broadband radiation) are similar to the ``grating anomalies'' discovered by Wood in 1902. The present analysis provides a simple physical interpretation of their presence in terms of the magnitudes and phases of the various orders of scattering. Simple relations for their dependence on the parameters are derived which agree in general with experimental results. Both the electromagnetic and acoustic cases are treated.
23(1952); http://dx.doi.org/10.1063/1.1701994View Description Hide Description
The Joule‐Thomson porous plug experiment is described, its quantitative aspects indicated, and the constant enthalpy condition set up. The experimental plan for the proposed measurement is described and a short analysis of the physical situation in the fluid given. The standard equation for the Joule‐Thomson coefficient is applied to the situation and details are given of how this equation may be integrated for two special physical situations. The information necessary for these integrations is discussed and physical means described for obtaining it. A numerical integration may be used for obtaining the work equivalent of heat (J) with a high precision corresponding to the high precision with which these various data may be measured.
23(1952); http://dx.doi.org/10.1063/1.1701995View Description Hide Description
It has been proposed that the conductivity of a porous semiconductor, such as oxide‐coated cathode, may be influenced by the presence of an electron gas in the pores of the aggregate. In this paper calculations for the magnitude of this component of the conductivity are made on the basis of two simplified models approximating the geometry of a pore. The conditions under which such a component of the conductivity can appreciably modify the total conductivity are analyzed. It is further shown that such a porous semiconductor will possess two sources of thermoelectric emf. A simple theory for the thermoelectric power of the electron gas in a pore is developed, and the manner in which it will combine with the normal thermoelectric power of the crystals is shown.
23(1952); http://dx.doi.org/10.1063/1.1701996View Description Hide Description
A study has been made of the thermoelectric power, the electrical conductivity, and the thermionic emission of (BaSr)O and BaO at different states of activation and on different base metals over a temperature range of 1100°K to 300°K. A plot of the logarithm of the conductivityvs reciprocal temperature showed two straight line regions. The temperature dependence of the thermionic emission was found to be the same as the temperature dependence of the conductivity in the temperature range 700°K to 1100°K. The slope of a plot of the thermoelectric power vs reciprocal temperature was also similar to the thermionic work function and the conductivityactivation energy in this temperature range.
The thermoelectric power varied with temperature from a value of about 2.0 mv/° at 1100°K, increasing to about 2.5 mv/° at 800°K, reducing to between 1.0 and 0.5 mv/° at about 500°K, and remaining practically constant or increasing slowly at still lower temperatures. In all thermoelectric power measurements the hot junction was positive indicating negative charge carriers.
The simple semiconductor theory does not adequately account for these results which seem to be in good agreement with the pore conduction hypothesis.
23(1952); http://dx.doi.org/10.1063/1.1701997View Description Hide Description
A process is described whereby the complex wave equation is transformed into an integro‐differential equation in a single real dependent variable. This makes possible a technique for obtaining wave functions, which is believed to offer definite advantages in some instances where the more standard methods are difficult to handle, e.g., in regions where the complex index is varying rapidly. The index may be entered in a tabulated form, and its exact analytical expression is not required.
The technique is then demonstrated by computing the reflection coefficient associated with an extremely critical region, that which one encounters at the ``fourth reflection condition,'' where the refractive index goes through a sharp peak (see reference 3).
A Note on the Approach of Narrow Band Noise after a Nonlinear Device to a Normal Probability Density23(1952); http://dx.doi.org/10.1063/1.1701998View Description Hide Description
The output of a low pass filter preceded by a nonlinear device excited by a noise source is given in terms of an integral equation. The first three central moments of the probability density of the output signal are obtained from the integral equation and the approach of these moments to those of a Gaussian or normal density is demonstrated.
23(1952); http://dx.doi.org/10.1063/1.1701999View Description Hide Description
Barium sulfide has been prepared in a form suitable as a cathode emitter as well as in the form of compressed pills. It has a work function of 2.1 ev with a wide variation possible in activation. The most active materials had an emission at temperatures of 900°K and greater comparable to that from pure BaO. Pure nickel and platinum only were used as base metals. An equimolar mixture of BaS‐SrS had a work function of 2.6 ev, and x‐ray analysis indicated solid solution formation. The electrical conductivity of BaS was found to vary between wide limits depending on the degree of activation and the denseness of the specimen but was much less than for BaO. At 1000°K the specific conductivity of a compressed pill was 10−5 ohm−1 cm−1. The thermoelectric power was found to be constant with temperature although it decreased with increase in the activity of the specimen. The warmer electrode was always positive. Pure BaS had a thermoelectric power of 2.5 mv per degree between 970° and 1270°K. The effect of added impurities of iron on the electrical characteristics was studied. By mass‐spectrometer studies, the evaporation rate of BaS was found to be much less than that of BaO, indicating a vapor pressure of the sulfide about 100 times less than that of the oxide. The heat of sublimation was found to be 104 kcal/mole.
23(1952); http://dx.doi.org/10.1063/1.1702000View Description Hide Description
First‐order perturbation theory is used to evaluate the scattered power at a receiver resulting from random inhomogeneities in the propagating medium. The integral expression for this scattered power is equivalent to the expressions as used by Pekeris and Booker and Gordon. However, it is shown that it is not appropriate to use a space correlation function of refractive index as defined by the above authors. Instead, this paper defines a time correlation function of refractive index which permits formal evaluation of the time average scattered power. It is also shown that, whereas a space correlation function of refractive index is not amenable to direct experimental evaluation, the time correlation function as defined in this paper is directly measurable. Finally, it is shown that for so‐called small‐scale turbulence the average scattered power does not depend appreciably on any particular model of atmospheric turbulence, whereas for large‐scale turbulence the frequency and scattering angle dependence of the scattered energy is affected greatly by the particular time correlation function chosen or by the assumption that scattering is the result of randomly located spheres.
23(1952); http://dx.doi.org/10.1063/1.1702001View Description Hide Description
Gaseous phenomena induced by short‐duration sparks at atmospheric pressure have been photographed during the first microseconds of their existence by a flash‐schlieren technique. The growth of the heated gas domain (kernel) expanding from the sparkdischarge has been observed for air and argon. The kernel continues to expand rapidly, but subsonically, after the spark current ceases and after the shock wave separates. It develops further into a torus about the sparkelectrodes and eventually decays. The development of flame from a heated gas kernel in a flammable mixture is illustrated. Energy relationships for the expanding argon kernel are discussed.
23(1952); http://dx.doi.org/10.1063/1.1702002View Description Hide Description
General formulas are derived for the shift in x‐ray diffraction maxima due to small distortions in simple cubic crystals. The special case of radial distortions due to lattice defects is considered in detail; it is found that the relative change in lattice constant computed from the shift in diffraction maxima is of the order of magnitude of the defect concentration and larger by as much as 100 percent than the linear expansion when the concentration of defects is of the order of one percent or less. A comparison is made of lattice constant, linear expansion, and density expected in crystals containing Frenkel defects,Schottky defects, or F centers.
23(1952); http://dx.doi.org/10.1063/1.1702011View Description Hide Description
Unsupported films of nitrocellulose of 0.25 micron and less in thickness bonded immediately and spontaneously in air to solid surfaces which they were made to touch. Bond strength increased with diminishing film thickness. Similar behavior was shown by films of gold, regenerated cellulose, polymethyl methacrylate, and gelatin. This bonding power of nitrocellulose films, which was apparently not attributable to static electricity or to mechanical joint formation, was lost while immersed in water, benzene, or hexane, but was regained upon removal and drying.
23(1952); http://dx.doi.org/10.1063/1.1702023View Description Hide Description
Complete and quantitatively accurate solutions of the properties of electrically short transmitting and receiving antennas (of length 2h such that 2πh/λ0≦1) are obtained by determining the distributions of current that actually satisfy the integral equations. Components of current in phase and in phase‐quadrature with the driving voltage or the incident electric field are evaluated together with the impedance, the effective length, and the gain. It is shown that when the King‐Middleton method of solving Hallén's integral equation by iteration is applied correctly, quite accurate results are obtained even in a first‐order solution. The greatest error in the first‐order formulas is shown to be in the resistance, a small quantity of higher order compared with the reactance. The newly determined values are combined with the King‐Middleton second‐order results to obtain more complete and more accurate impedances and effective lengths in the range of 0≦2πh/λ≦1.4.
23(1952); http://dx.doi.org/10.1063/1.1702027View Description Hide Description