Index of content:
Volume 6, Issue 1, 01 January 1935

Instantaneous Speeds in Air of Explosion Reports at Short Distances from the Source
View Description Hide DescriptionIn the first series of measurements the source was one No. 6 blasting cap, while in the second series one pound of 50 percent nitroglycerine stick dynamite was used as source. A telephonecarbon button microphone was the receiver and was held fixed in location while shots were fired successively at 5, 8, 12.5, 25, 35, 50, 100 and 600 meter distances. A two‐element string oscillograph was used for timing, one element recording the instant of firing, the other element recording the arrival of the wave at the microphone. The work was done at time of no perceptible wind; air temperatures were measured carefully; no humidity measurements were made. Travel times could be read reliably to 10^{−4} second and distance measurements were at least correspondingly good. Instantaneous speeds were obtained by plotting time computed minus time observed against distance and measuring slopes of the resulting curve. Since this work was incidental to seismicprospecting, the observations were not quite as numerous as those of von Angerer and Ladenburg. However, the results are similar as regards abnormally high speeds near the source. Also, the use of instantaneous speeds appears to show abnormally low speeds a little farther from the source, perhaps masked in the work of von Angerer and Ladenburg due to the use by them of average speeds instead of instantaneous speeds.

Shot Effect and Thermal Agitation in an Electron Current Limited by Space Charge
View Description Hide DescriptionExperimental evidence is presented which shows that shot effect is decreased by space charge and that the internal impedance of a vacuum tube is subject to thermal agitation.

The Potential Distribution Between Parallel Plates and Concentric Cylinders Due to Any Arbitrary Distribution of Space Charge
View Description Hide DescriptionEquations are derived for the electric potential and field intensity due to a distribution of space charge in a slab of dielectric between two infinite parallel conducting plates. The charge density may be any integrable function of the coordinate perpendicular to the plates. The corresponding solution for concentric cylinders is also given. A number of special cases are discussed, including that of a uniformly distributed charge, and one of sinusoidal distribution. The latter has an application in the theory of the piezoelectric resonator.

Potential Distributions About an Infinitely Extended Line Electrode on the Surface of a Horizontally Stratified Earth. II
View Description Hide DescriptionThe analytical theory is given for the potentials and gradients to be found on the surface of a horizontally stratified earth in which the current source is an infinitely extended cable or line electrode lying on the surface. Power series expansions in the distance from the electrode are derived for small distances and asymptotic expansions for large distances. Detailed treatments are given for the two layer earth, for all thicknesses of the surface layer, and for the three layer earth in which the thickness of the second layer either equals or is twice as great as that of the surface layer, as well as formal expansions for general many layered earths. Simple closed hyperbolic function expressions are derived for the surface gradients for three layer systems in which the lowest layer is either of infinite or zero conductivity. The solution for the direct interpretation problem in which the continuous vertical conductivity variation may be determined from a knowledge of the surface gradients is briefly outlined, following the method of Slichter and Langer for the case where the current source is a point electrode. The analytical results of the indirect interpretation problem for a stratified earth are illustrated by thirty numerical and graphical examples.

A Note on Mixed Boundary Value Problems in Logarithmic Potential Theory
View Description Hide DescriptionA method is given for solving logarithmic potential problems in which the potential is preassigned over part of the boundary and the normal derivative over the remainder. A ``mixed'' Green's function is defined such that it vanishes over part of the boundary of interest and its normal derivative vanishes over the remainder, and the solution for the logarithmic potential is expressed in terms of this function and the boundary conditions by means of Green's theorem. Taking the case of the infinite quadrant as the ``prototype'' region the solutions for other regions such as the infinite half plane, infinite and semi‐infinite strips, and the circle are obtained by mapping them on the infinite quadrant; these are illustrated by several specific examples.

On Electric Charges of Disperse Systems Which Are the Seats of Physico‐Chemical Reactions
View Description Hide DescriptionIn a number of previous papers a mathematical study was made of small drops, which either absorb or produce some substances by virtue of physico‐chemical reactions. This creates in the drop and in the surrounding medium gradients of concentrations of corresponding substances. In this note it is pointed out that when the reacting substances are ionized, these gradients will result in the appearance of electric charges and electric fields. An estimation shows that they are quite comparable with electric charges, produced by other factors in disperse systems. The fundamental property of the charges here considered is that they disappear as soon as the reactions cease. Their importance in biological systems is pointed out.

The Mechanism of Division of Small Liquid Systems Which Are the Seats of Physico‐Chemical Reactions II. Instability of Two‐Phase Systems
View Description Hide DescriptionIn continuation of a previous paper, the same mathematical method is applied to a system, consisting of two spherical concentric drops, under the assumption, that a reaction takes place only in the outer larger drop, but not in the inner one. It is found, however, that even in that case the inner drop may become unstable for infinitesimal deformations, and spontaneously elongate.

The Flexure Problem for Rectangular Beams with Slits
View Description Hide DescriptionExperimental and approximate theoretical studies, made at the United States Forest Products Laboratory, Madison, Wisconsin, show that the mean shearing stress in the neutral plane of a rectangular beam with symmetrical horizontal slits or checks extending along its lateral faces is less than that given by the usual engineering formulas; that is, there is a definite ``two‐beam'' action which relieves the shearing stress in the portion of the beam weakened by the slits. This paper presents an exact solution of the flexure problem for a beam of such section and confirms the main features of the distribution of shearing stress found in the earlier investigation. The solution of the flexure problem requires the solution of Laplace's equation within the plane region coincident with a cross section of the beam, subject to certain boundary conditions. This solution is obtained by using the Schwartz‐Christoffel transformation of a polygon onto a half‐plane and solving the transformed boundary value problem. The exact solution is set up as an infinite series. To simplify the calculations two approximate solutions are also obtained, one of which is used in treating a numerical example.

A Determination of the Refractive Index of Vitreous Silica and the Calibration of Silica Refraction Thermometers Between 18° and −200°C
View Description Hide DescriptionThe variation with temperature of the refractive index of fused silica for the helium line 5877.2A has been determined between 18° and −200°C and the results have been applied to the calibration of vitreous silica refraction thermometers at low temperatures. These data have been correlated with measurements at high temperatures. It is found that the refractive index between −200°C and 1000°C can be represented by the equation .

Magnetic Susceptibility of Some Alloys of ``Gamma‐Brass'' Structure
View Description Hide DescriptionThe change of diamagnetic susceptibility with composition of a number of phases of gamma‐brass structure (Cu–Zn, Cu–Cd, Ag–Zn, Ag–Cd) has been determined. In each case when the phase makes its first appearance with low electron ratio, it is not strongly diamagnetic, but the increase in diamagnetism is approximately lineally dependent on the number of free electrons, and the strongest diamagnetism occurs at the limit of the gamma‐phase with the highest electron ratio possible for the structure.