Volume 18, Issue 11, 01 November 1947

Initial Oscillation on a Rotational Viscometer
View Description Hide DescriptionThe oscillatory system of a rotational viscometer has been investigated. The oscillation equations were checked with experimental bob deflection‐time curves obtained for Newtonian liquids.
To be able to rapidly obtain correct values when taking flow curves the oscillatory system should be critically damped. Since this condition cannot be easily obtained in practice, the system should be slightly overdamped, meaning that the inertia (I) should be equal or smaller than πμ^{2}/720KS ^{2}. It is shown that due to the higher viscosity of thixotropic materials at lower rates of shear, the flow curves at these rates of shear give an indication of rather too low than too high shearing stresses.

Stability and High Frequency
View Description Hide DescriptionIn a linear oscillator which is not conservative, let the frequency vary so as to tend to infinity when time increases indefinitely. It seems to be evident that the oscillations must then be of stable type. Actually, this is not true. The paradox results from the circumstance that the relevant criterion of stability depends on the monotone decrease, rather than on the indefinite decrease, of the instantaneous period.

Mechanism of Fracture of Glass and Similar Brittle Solids
View Description Hide DescriptionA theory is proposed which connects the stress, f, required to break a brittle material in simple tension, with its duration of application, t. The slow process preceding fracture is shown to be the orientation of the atomic network contained in an elementary prism of length r=λ_{0} E/f, where E is Young's modulus and λ_{0} is the critical elongation required for fracture. The rate‐controlling factor is the activation energy,Eα/f, for the orientation or rearrangement of the atomic network under the stress, f. Moisture on glass, and moisture plus oxygen on certain metals, are important catalytic or fatigue‐promoting factors because they reduce the unit activation energy, α. The theory leads to the equationsand,where t is the time for fracture (duration of the stress), k is the Boltzmann constant, T the absolute temperature, and α and k _{0} are experimentally determined constants. The logarithmic expression has the same form as the Glathart‐Preston [J. App. Phys. 17, 189 (1946)] empirical relation logt= −a/m+1/fm, which, in the case of glass, appears to be valid over a time factor of 10^{7}.
The theory shows why a solid object does not have a single characteristic breaking strength, and how it adjusts its fracture mechanism to whatever stress is applied. Quantitative tests of the theory are made, using fracture data on various glasses and on one glass at various temperatures. Applicability of the theory to certain aspects of fatigue of metals under stress‐corrosion conditions, as well as to failure by fracture of the more rigid organic plastics, is indicated.
An equation,Eλ_{0}=2γ, is proposed which connects Young's modulus and the critical fracture distance with the surface tension, γ, of the solid. Some examples are given.

Acceleration of Electrons by a Resonant Cavity
View Description Hide DescriptionElectrons were accelerated by means of a single resonant cavity operating at 75‐cms wave‐length. Energies as high as 0.75 Mev were attained by single‐stage acceleration, the electrons entering the cavity at virtually zero velocity. By turning the emergent beam about, and reinjecting it into the cavity in the opposite direction two stage acceleration was achieved and 1.25‐Mev electrons were produced. Possibilities of a ``shuttle accelerator'' are discussed.

Infra‐Red Spectra of Hydrocarbons: II. Analysis of Octane Mixtures by the Use of Infra‐Red Spectra Obtained at Low Temperatures
View Description Hide DescriptionInfra‐red spectra in the region 2 to 22 microns were obtained for the four trimethylpentanes, at temperatures of 0°C and −195°C. In agreement with theory, the band ``widths'' at −195°C are roughly half as great as at 0°C. The spectra were observed experimentally by condensation of a film of the hydrocarbon on the reflecting bottom surface of a cell mounted vertically, with its lower end immersed in ice or liquid nitrogen. A method of forming films of reproducible dimensions and thickness is described.
To provide a quantitative estimate of the advantage for analytical purposes of the use of spactra obtained at low temperatures, an expression is derived which gives the probability (for random distribution of the band positions) that at least one band can be found for each component of a mixture, which does not ``overlap'' bands of the other components. Application of the formula, with some simplifying assumptions, to a mixture of the 18 octane isomers, indicates that reduction of the band ``width'' from 40 cm^{−1} to 20 cm^{−1} (corresponding to the temperature change from 0°C to −195°C) increases the calculated probability of the existence of a ``non‐overlapped'' band for at least 17 of the isomers from 0.003 to 0.999. The importance of this result in infra‐red analyses is pointed out.
The use of spectra obtained at liquid helium temperatures is suggested as offering attractive possibilities for the analysis of complex mixtures.

Magnetic Field Configurations Due to Air Core Coils
View Description Hide DescriptionThe field configurations around a circular loop of wire bearing current are discussed, and a tabulation is presented for the field component parallel to the axis of the loop. Formulae are derived for the current distribution which must obtain in cylindrical and ellipsoidal coils in order that the field inside be uniform. Several special cases are noted. The energy storage in the return flux is evaluated in each case.

Design of an Air Core Synchrotron
View Description Hide DescriptionThe analysis of the preceding paper is applied to the problem of designing a synchrotron in which the magnetic fields are produced by air core coils. The air core synchrotron is shown to be practical and to present certain advantages.

A Sound Velocity Method for Determining the Compressibility of Finely Divided Substances
View Description Hide DescriptionA method is presented whereby the adiabatic compressibility of a finely divided material can be found from sound velocity and density measurements of a suspension of the particles in a liquid. The method is based on the assumption that the velocity of sound in a suspension is the same as it would be in an ideal solution of the two substances. This is verified experimentally by measurements of sound velocity in kaolin‐water suspensions and xylene‐water emulsions, and the method is illustrated by the determination of compressibility of the oil droplets in an oil emulsion and of the blood corpuscles in horse blood. Considerable accuracy is attainable for materials which are not too incompressible compared to the suspending liquid.

End‐Effect in Rotational Viscometers
View Description Hide DescriptionIn the classical equations for the traction on concentric cylinders by a viscous substance, it is assumed that traction on the top and bottom of the inner cylinder (bob) is negligible in comparison with that on the curved surface. In viscometers of practical dimensions, however, it is necessary to compensate for the end‐traction or end‐effect by adopting one of several expedients in design or by determining the magnitude of the effect and accounting for it in terms of increased length of bob.
In the experiments reported in this paper, the method of multiple bobs has been used, and the variation of end‐effect with the following factors studied: (1) radius of bob; (2) clearance between cylindrical surfaces; (3) separation between bottom of bob and cup; and (4) viscosity.
The magnitude of the end‐effect increases with radius and with clearance. For separations at the bottom greater than 1 cm and for viscosities above 1 poise the end‐effect is nearly constant, but must be determined for each cup and bob combination. At lower viscosities the correction must be determined either by calibration with a standard liquid of about the same viscosity as the unknown, or by the multiple‐bob method.
It is shown that trapping a layer of air beneath the bob is not effective in making the traction on the bottom negligible. The end‐effect is almost as large for a bob with an open bottom as for a closed one.
When the method of multiple bobs is used, data with an accuracy of ±2 percent can be obtained without calibration. When the instrument constant is determined with standard liquids or computed from a value for the end‐effect previously found, data of somewhat lower accuracy result, but the uncertainty should be within ±5 percent.

The Theory of Disk‐Loaded Wave Guides
View Description Hide DescriptionThe properties of circular wave guides loaded with apertured disks are discussed both qualitatively and quantitatively. Formulae and curves are given for various quantities including the wave and group velocities, the attenuation, and the power flow.

Equations for the Inductances of Three‐Phase Coaxial Busses Comprised of Square Tubular Conductors
View Description Hide DescriptionEquations are derived for calculating the associated inductances of the conductors of three‐phase coaxial busses comprised of square tubular conductors. It is assumed that the conductors are nonmagnetic, are of such lengths that end effects are negligible, are right‐cornered, and carry currents uniformly distributed over their cross sections. The general equations are obtained through use of geometric mean distance theory. Approximate equations, the conductors being considered as indefinitely thin, are epitomized in a table which yields values sufficiently accurate for most design work. In turn, these approximate equations are reduced to simple equations which also yield values sufficiently accurate for much design work. These equations for inductance lead to corresponding equations for the reactive voltage drops. Use of these various equations and the relative accuracy to be expected of them is illustrated by calculating the inductances and reactive voltage drops of typical busses.
The changes in the inductances due to rounding the edges of the conductors and the changes produced in both the inductances and the resistances by skin and proximity effects are investigated. The changes in the inductances due to rounding the edges can be approximated by use of a known equation. The changes in the inductances due to power frequency skin and proximity effects prove to be negligible; the changes in the resistances can be calculated by use of known skin‐effect factors and newly derived proximity‐effect factors.
Calculation of the inductances of three‐phase coaxial busses constructed of tubular conductors made up of two channels or angles placed flange to flange is discussed. Finally, attention is called to a relatively little known means of obtaining balanced three‐phase operation of geometrically unbalanced three‐phase busses.

Mechanical Behavior of High Damping Metals
View Description Hide DescriptionThe relation between the various measures of internal friction are independent of the precise mechanism of the dissipation of energy when the internal friction is small, but not when it is large. In this paper the relation between the two measures most commonly used, logarithmic decrement and tangent of the angle with which strain lags behind stress, is deduced for all levels of internal friction in the important case in which the dissipation of energy is due to a relaxation process having a single time of relaxation. The conditions are further derived under which a specimen of such a metal will not vibrate, but returns aperiodically to its equilibrium configuration.

The Field of a Microwave Dipole Antenna in the Vicinity of the Horizon. II
View Description Hide DescriptionIn this paper the results of a previous investigation are extended to include cases where the elevation of the transmitter z _{1}, or of the receiver z, is less than about 1 when expressed in natural units of height. When z _{1} < 1 and z > 1 the electromagnetic potential ψ in the vicinity of the horizon is given, in the case of strong absorption (β≫1), by,where,and the notation of I is used. Expression (a) equals expression (B) or (C) of I multiplied by the factor (1+βz _{1}).
When both z _{1} and z are less than about unity the potential is given by,where L is the natural unit of horizontal distance. Expression (c) is equal to the expression for the surface wave given in (D) of I multiplied by the factor (1+βz _{1})(1+βz).
 LETTERS TO THE EDITOR


Grain Growth in Alpha‐Brass
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Comments on ``Grain Growth in Alpha‐Brass''
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Electron Microscope and Electron‐Diffraction Study of Slip in Metal Crystals
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