Volume 19, Issue 1, 01 January 1948
Index of content:
19(1948); http://dx.doi.org/10.1063/1.1697867View Description Hide Description
The slipperiness of graphite is not inherent in the crystal structure alone but depends upon adsorptionfilms, especially water, which cover the carbon atoms and provide surfaces of low cohesion. In vacuum graphite rods or brushes seize upon a moving base (copper or graphite) and wear away as a fine dust. This wear and accompanying high friction are instantly stopped by some condensible vapors at low pressures (H2O, C6H6, NH3, etc.) which apparently effect the coverage of the graphite by a reversible adsorption governed by the pressure and surface temperature. Under conditions of optimum coverage (zero wear) the graphitefriction is still appreciable but may be accounted for as the heat of cohesion of water monolayers attached to the carbon atoms and undergoing successive makes‐and‐breaks. From the measured frictional energy and an assigned heat of cohesion based upon surface energy data, the area of molecular contact is estimated to be 4×10−6 cm2 under a real pressure 2×104 kg/cm2.
The wear dust of unlubricated graphite shows a unique adsorptive power at room temperature, greater for hydrogen than that of activated charcoal by five orders of magnitude. This and other characteristics may throw new light upon the mechanism of friction in general and upon the structure of stroked graphitesurfaces in particular.
19(1948); http://dx.doi.org/10.1063/1.1697866View Description Hide Description
The following report deals with a method of calculating the admittance of dipoles that consist of complete cones of wide angle. The theory makes use of the orthogonal properties of Legendre's functions and of their derivatives in order to make the outside field's tangential component vanish over the spherical end surfaces of the dipoles, and to make the inside and outside fields fit at the boundary sphere. This is a surface of the same radius as the dipole, extending from the upper to the lower end surface.
This leads to a set of Eqs. (10) for the infinite set of coefficients bk , and an Eq. (3) that expresses the effective load admittance yt in terms of the coefficients bk . If a sufficient number of these coefficients is considered, there should be no appreciable discontinuities in field at the boundary sphere, and the tangential field should vanish on all the surfaces of the dipole.
On the assumption that only the first two outside waves, and the internal T.E.M. and first higher order inside wave are important for dipoles whose radius is less than a half‐wave‐length, an approximate formula for yt is found, and the results are shown in Figs. 4 and 6. It is unnecessary to evaluate the solutions of Legendre's equationLn (θ), because the integrals that involve them are expressed in terms of n(μ1) and dn(μ1)/dμ1, n being the root of Ln (A)=0, and μ1=cosA.
The solutions are transformed to the center of the dipole, and plotted in Fig. 6, while the relative terminating admittances, K·yt , are plotted on an impedance diagram in Fig. 7.
19(1948); http://dx.doi.org/10.1063/1.1697868View Description Hide Description
A basic theory of slots in rectangular wave‐guides is given. The analogy with a transmission line is developed and established, and detailed formulae for the reflection and transmission coefficients and for the ``voltage amplitude'' in the slot generated by a given incident wave are given. While the complete expressions for these quantities are quite complicated and involve the summation of infinite series, certain parts of the expressions are comparatively simple. In particular, the ``resistance'' or ``conductance'' of slots which are equivalent to series or shunt elements in a transmission line are given by fairly simple closed expressions. Guide‐to‐guide coupling by slots and slot arrays are also considered. A more detailed summary of the main results of the paper is given in Section 1.
19(1948); http://dx.doi.org/10.1063/1.1697869View Description Hide Description
The scattering of a TE1, 1wave by a thin, perfectly conducting circular ring suspended in a circular wave guide with perfectly conducting walls is considered, and approximate expressions are obtained for the scattering cross section, resonance maximum, and half‐width as a function of the width of the ring.
19(1948); http://dx.doi.org/10.1063/1.1697870View Description Hide Description
A folded rectangular wave guide cavity,resonant at a frequency of 2800 megacycles, is used to accelerate electrons which are injected at 2000 volts energy to an energy of 300 kilovolts. Three accelerating stages are provided, the power source being a type 4J33 radar magnetron operating on a duty cycle of 2×10−4. Power output of the magnetron is 800 kilowatts, the power consumed by the cavity being approximately 250 kilowatts. Design data for the cavity are obtained from slotted wave guide models of the cavity sections.
Temperature Coefficient of Electrical Resistivity for Crystalline Selenium Containing Various Percentages of Bromine19(1948); http://dx.doi.org/10.1063/1.1697871View Description Hide Description
The temperature coefficient of electrical resistance of brominated selenium over the temperature range −30°C to 100°C was found to be negative and variable. The electrical resistivities of the selenium samples varied by factors of three to twelve for the temperature range mentioned, depending upon the bromine content. A reproducible hysteresis loop was obtained on the plot of resistivityversus temperature. A minimum in the plot of electrical resistivityversus bromine content was found with 0.007 percent bromine in selenium. Activation energies for freeing electrons obtained from the slopes of conductivityversus temperature plots indicate a dependence upon bromine content in the selenium.
19(1948); http://dx.doi.org/10.1063/1.1697872View Description Hide Description
When the transient response of a linear network to an applied unit step function consists of a monotonic rise to a final constant value, it is found possible to define delay time and rise time in such a way that these quantities can be computed very simply from the Laplace system function of the network. The usefulness of the new definitions is illustrated by applications to low pass, multi‐stage wideband amplifiers for which a number of general theorems are proved. In addition, an investigation of a certain class of two‐terminal interstage networks is made in an endeavor to find the network giving the highest possible gain—rise time quotient consistent with a monotonic transient response to a step function.
19(1948); http://dx.doi.org/10.1063/1.1697873View Description Hide Description
A divergence expression for the ratio of energy per steradian reflected from a smooth curved surface to that incident on the surface is derived. It generalizes previous results in that the source and point of observation may both be at finite distances from the reflecting surface. No restrictions are placed on the angles of incidence and reflection except that they be equal. The only limitation placed on the analytical accuracy of the geometrical result is that the surface be sufficiently smooth so that the principal radii of curvature are defined at the point of reflection. It is required, of course, that the wave‐length of the energy shall be small compared to the principal radii of curvature of the surface, in order that the geometrical result may be interpreted as a divergence formula. All of the previous results on this problem known to the authors are derived as special cases. Application of the result in connection with the spreading of radio rays by the curvature of the earth leads to somewhat simpler formulas than now available.
19(1948); http://dx.doi.org/10.1063/1.1697874View Description Hide Description
Expressions are derived for a system of n compartments whereby the amount of a substance S which has moved from any one compartment to any other can be determined in a single experiment from measurements of the amounts of n tagged species in the individual compartments. It is shown that n individual species of S are required which must be uniformly mixed and behave identically but must be distinguishable by the observer. The application of the equations to studies using multiple isotopic tracers is described, and the special case of a two compartment system is analyzed in detail.
19(1948); http://dx.doi.org/10.1063/1.1697875View Description Hide Description
This note gives a theoretical solution to a plate containing two circular holes of equal size. The method of solution is to add to the given stress system a suitable biharmonic function which gives no stress at infinity. The parametric coefficients involved in the solution are adjusted so as to satisfy the boundary conditions at the edges of the holes. Bipolar coordinates are used in the solution, by means of which explicit expressions are obtained for the parametric coefficients. Three fundamental stress systems are discussed in some detail, namely, the all‐around tension case, the longitudinal tension case, and the transverse tension case. Formulas of the stress along the edges of holes are derived and, in particular, values of maximum stress are calculated. The limiting case in which the holes are tangential is also discussed.
An Alignment Chart Giving the Polarization Correction of Equi‐Inclination Weissenberg Photographic Intensities19(1948); http://dx.doi.org/10.1063/1.1697876View Description Hide Description
A nomograph is presented which gives, in terms of film coordinates μ and Υ, the polarization factors to be applied to intensities taken from equi‐inclination Weissenberg photographs to correct them for polarization. The remaining correction, the Lorentz factor, merely involves division by cos2μ sinΥ.
19(1948); http://dx.doi.org/10.1063/1.1697877View Description Hide Description
Simplified directions are given for the making of alignment charts from equations in three variables. A fixed determinant is used to put the equation in determinantal form. The determinant is manipulated to put it in standard line form; three standard types of distortion factors are used to produce a chart of convenient shape.
19(1948); http://dx.doi.org/10.1063/1.1697878View Description Hide Description
A helix is a fundamental form of antenna with many radiation modes. A recently reported mode, called an axial or beam mode, occurs for a relatively wide range of helix dimensions, in the region of 0.2 to 0.5 wave‐lengths diameter and as high as 0.5 wave‐lengths spacing between turns. The radiation is maximum in the direction of the helix axis and is nearly circularly polarized. This mode may persist with a given helix over a considerable frequency range. In this range the phase velocity of wave propagation along the helical conductor is reduced. An approximate expression for the field pattern of a single turn helix is developed. The pattern of a helix of a number of turns is then calculated as an array of such turns. Measured and calculated patterns show good agreement.
19(1948); http://dx.doi.org/10.1063/1.1697879View Description Hide Description
Data obtained from sedimentationvelocity and viscosity measurements on a series of cellulose acetate fractions in acetone are interpreted in terms of two models, the impenetrable ellipsoid of rotation and the uniform density random coil. The lack of agreement using the former model is shown to be a real effect, rather than one determined by experimental inaccuracy. As other investigations have revealed, the uniform density random coil is not a satisfactory model for these molecules either. Probably the best hydrodynamical model for these and other extended but not perfectly rigid molecules in solution is a penetrable ellipsoid of rotation.
The Effect of Ground Constants on the Characteristic Values of the Normal Modes in Non‐Standard Propagation of Microwaves19(1948); http://dx.doi.org/10.1063/1.1697859View Description Hide Description
It is shown that for the case of a strongly absorbing ground (β≫1) the characteristic values D of the normal modes are given by[Formula ID: E1],where
[Formula ID: E2],Da is the characteristic value obtained under the usual assumption that the height‐gain function U vanishes at the ground, and U̇ denotes dU/dz at z=0. In the other limit of a perfectly conducting ground (β≪1) the following expansion holds
[Formula ID: E3],where Dc is the characteristic value obtained under the condition U̇(0)=0. Since U̇ and U in (a) and (c), respectively, are known from the normalization condition, it is possible to determine the first correction terms to the characteristic values in each case.
Errata: The Electrostatic Field of a Point Charge inside a Cylinder, in Connection with Wave‐Guide Theory19(1948); http://dx.doi.org/10.1063/1.1697860View Description Hide Description
19(1948); http://dx.doi.org/10.1063/1.1697861View Description Hide Description
The analysis of anaeroid capsule performance by the expansion of the observed pressure‐deflection curve in Gram summation‐orthogonal polynomials is illustrated on a series of fifteen runs on five typical capsules.
All of the deflection curves examined contained significant cubic and quartic terms while a few showed fifth‐order terms. These high order terms are very unstable in magnitude and sign for successive deflections of the same capsule, and this accounts for the very complex hysteresis curves which have been observed.
The relationship of these high order terms in the deflection characteristic to the accuracy and cost of precise anaeroid barometers is brought out, and it is suggested that barometric systems free of elastic redundancies must be devised if accurate barometers for radiosondes and similar instruments are to be mass produced.
19(1948); http://dx.doi.org/10.1063/1.1697864View Description Hide Description