Volume 4, Issue 4, 01 April 1933
Index of content:
4(1933); http://dx.doi.org/10.1063/1.1745169View Description Hide Description
An analytical study is made of the potential distribution about an electrode on a stratified earth, from the point of view of developing special formulas appropriate for computation at small and large distances from the electrode. Power series in the distance for small distances and simple asymptotic expansions for large separations are derived first for a two layer earth, from integral expressions for the potentials. For graphical integration a transformation is derived which makes the integrals converge very rapidly. For a many layer earth a general method for deriving the power series for small distances is indicated. For large distances, general expansions are given in closed (Eq. (23)) and asymptotic forms (Eq. (24)) applying to all types of conductivity variation. Explicit expressions for the power series are given for a three layer earth with the middle layer of thickness equal to and twice that of the upper layer. Closed and very rapidly converging series of Hankel function expansions are then developed for the third layer having zero or infinite conductivities, with the thickness of the middle layer being equal to, twice and three times that of the upper layer. Thirty numerical cases have been computed and plotted as curves to illustrate the fundamental formulae developed. In an appendix general proofs are given for the asymptotic expansions of not only the type of integrals occurring in the present problem but also for integrals involving Weber and Hankel functions as well as the Bessel functions, and where these functions are of non‐zero orders.
4(1933); http://dx.doi.org/10.1063/1.1745170View Description Hide Description
A method capable of solving x‐ray powder photographs derived from crystal structures of low symmetry has been described. By the use of this method, the crystal structure of uranium has been obtained. Uraniumcrystallizes according to space group C 2h 3 of the monoclinic system, with 2 atoms in each crystallographic cell. The dimensions of the cell are: a=2.829A, b=4.887A, c=3.308A. Axial ratios are: 0.5791 : 1 : 0.6771. The x‐ray density of uranium is 19.05. The uranium atoms appear to be prolate spheroids with 3.425A as the major axis and 2.826A as the minor axis.
4(1933); http://dx.doi.org/10.1063/1.1745171View Description Hide Description
A series of well annealed iron‐nickel alloys in nominal steps of 10 percent Ni, including pure iron and pure nickel, has been examined for the effect of pressures, up to 12,500 kg/cm2, on the magnetic flux density. The application of pressure to a well annealed specimen causes a relatively large change in flux, usually a decrease and an incomplete recovery on release of pressure. The recovery is reversible in the sense that the same curve of flux change is traced with each series of pressure applications, provided the measuring pressure does not exceed that first applied. The 30 percent Ni alloy is rendered nearly nonmagnetic by a pressure of 12,000 kg/cm2. In the remaining metals pure iron exhibits the greatest and 90 percent Ni the smallest pressure change of flux. At constant field the different alloys exhibit various types of pressure changes of flux; linear, nonlinear and types exhibiting hysteresis.
4(1933); http://dx.doi.org/10.1063/1.1745172View Description Hide Description
The sensitivity of the gravity balance described in the March, 1932, number of Physics is such that a correction must be made for the effect of the attraction of the moon. This lunar effect has been measured by hourly readings over one complete cycle and agrees, within the observational error, with the effect calculated for the vertical component of the pull of the moon without any compensation for the centrifugal effect of the earth's motion around the center of gravity of the system. The effect has a period of 24.8 hours and not 12.4 hours as the tides, there is no trace of the twelve‐hour period. Values of gravity plotted against time follow accurately a sine curve which shows a small time lag as compared with the theoretical curve. This does not seem to be accidental but has not been explained.
4(1933); http://dx.doi.org/10.1063/1.1745173View Description Hide Description
The snake is replaced by a model consisting of a number of spools separated by light pins and held together by rubber bands. The forces that act on one spool are considered. If the spool is in equilibrium between curved guides, and if the tensions in the rubber bands are altered in such a way that there is no change in the resultant longitudinal forces, but that the curvature of the given part of the model tends to increase, it is shown that there is a tendency to slip along the guides toward a region where the curvature is greater.